Author: IMC

When children start school, they learn how to recite their numbers (“one, two, three…”) and how to write them (1, 2, 3…). Learning about what those numbers mean is even more challenging, and this becomes trickier yet when numbers have more than one digit — such as 42 and 608.

It turns out that the meaning of such “multidigit” numbers cannot be gleaned from simply looking at them or by performing calculations with them. Our number system has many hidden meanings that are not transparent, making it difficult for children to comprehend it.

In collaboration with elementary teachers, the Mathematics Teaching and Learning Lab at Concordia University explores tools that can support young children’s understanding of multidigit numbers.

We investigate the impact of using concrete objects (like bundling straws into groups of 10). We also investigate the use of visual tools, such as number lines and charts, or words to represent numbers (the word for 40 is “forty”) and written notation (for example, 42).

Our recent research examined whether the “hundreds chart” — 10 by 10 grids containing numbers from one to 100, with each row in the chart containing numbers in groups of 10 — could be useful for teaching children about counting by 10, something foundational for understanding how numbers work.

When children start learning about numbers, they do not naturally see tens and ones in a number like 42. (Shutterstock)

What’s in a number?

Most adults know that the placement of the “4” and “2” in 42 means four tens and two ones, respectively.

But when young children start learning about numbers, they do not naturally see 10s and ones in a number like 42. They think the number represents 42 things counted from one to 42 without distinguishing between the meaning of the digits “4” and “2.” Over time, through counting and other activities, children see the four as a collection of 40 ones.

This realization is not sufficient, however, for learning more advanced topics in math.

An important next step is to see that 42 is made up of four distinct groups of 10 and two ones, and that the four 10s can be counted as if they were ones (for example, 42 is one, two, three, four 10s and one, two, “ones”).

Ultimately, one of the most challenging aspects of understanding numbers is that groups of ten and ones are different kinds of units.

Numbers can be arranged in different ways

The numbers in hundreds charts can be arranged in different ways. A top-down hundreds chart has the digit “1” in the top-left corner and 100 in the bottom-right corner.

A top-down hundreds chart. (Vera Wagner), Author provided (no reuse)

The numbers increase by 10 moving downward one row at a time, like going from 24 to 34 using one hop down, for instance. A second type of chart is the “bottom-up” chart, which has the numbers increasing in the opposite direction.

A bottom-up hundreds chart. (Vera Wagner), Author provided (no reuse)

Counting by 10s

Children can move from one number to another in the chart to solve problems. Considering 24 + 20, for example, children could start on 24 and move 20 spaces to land on 44.

Another way would be to move up (or down, depending on the chart) two rows (for example, counting “one,” “two”) until they land on 44. This second method shows a developing understanding of multidigit numbers being composed of distinct groups of 10, which is critical for an advanced knowledge of the number system.

For her master’s research at Concordia University, Vera Wagner, one of the authors of this story, thought children might find it more intuitive to solve problems with the bottom-up chart, where the numbers get larger with upward movement.

After all, plants grow taller and liquid rises in a glass as it is filled. Because of such familiar experiences, she thought children would move by tens more frequently in the bottom-up chart than in the top-down chart.

 

Study with kindergarteners, Grade 1 students

To examine this hypothesis, we worked with 47 kindergarten and first grade students in Canada and the United States. All the children but one spoke English at home. In addition to English, 14 also spoke French, four spoke Spanish, one spoke Russian, one spoke Arabic, one spoke Mandarin and one communicated to some extent in ASL at home.

We assigned all child participants in the study an online version of either a top-down or bottom-up hundreds chart, programmed by research assistant André Loiselle, to solve arithmetic word problems.

What we found surprised us: children counted by tens more often with the top-down chart than the bottom-up one. This was the exact opposite of what we thought they might do!

This finding suggests that the top-down chart fosters children’s counting by tens as if they were ones (that is, up or down one row at a time), an important step in their mathematical development. Children using the bottom-up chart were more likely to confuse the digits and move in the wrong direction.

Tools can impact learning

Tools used in the math classroom can impact children’s learning. (Shutterstock)

Our research suggests that the types of tools used in the math classroom can impact children’s learning in different ways.

One advantage of the top-down chart could be the corresponding

Our research suggests that the types of tools used in the math classroom can impact children’s learning in different ways.

One advantage of the top-down chart could be the corresponding left-to-right and downward movement that matches the direction in which children learn to read in English and French, the official languages of instruction in the schools in our study. Children who learn to read in a different direction (for example, from right to left, as in Arabic) may interact with some math tools differently from children whose first language is English or French.

The role of cultural experiences in math learning opens up questions about the design of teaching tools for the classroom, and the relevance of culturally responsive mathematics teaching. Future research could seek to directly examine the relation between reading direction and the use of the hundreds chart.

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Credit of the article given to The Conversation

 

A pair of mathematicians studied the UK National Lottery and figured out a combination of 27 tickets that guarantees you will always win, but they tell New Scientist they don’t bother to play.

David Cushing and David Stewart calculate a winning solution

Earlier this year, two mathematicians revealed that it is possible to guarantee a win on the UK national lottery by buying just 27 tickets, despite there being 45,057,474 possible draw combinations. The pair were shocked to see their findings make headlines around the world and inspire numerous people to play these 27 tickets – with mixed results – and say they don’t bother to play themselves.

David Cushing and David Stewart at the University of Manchester, UK, used a mathematical field called finite geometry to prove that particular sets of 27 tickets would guarantee a win.

They placed each of the lottery numbers from 1 to 59 in pairs or triplets on a point within one of five geometrical shapes, then used these to generate lottery tickets based on the lines within the shapes. The five shapes offer 27 such lines, meaning that 27 tickets will cover every possible winning combination of two numbers, the minimum needed to win a prize. Each ticket costs £2.

It was an elegant and intuitive solution to a tricky problem, but also an irresistible headline that attracted newspapers, radio stations and television channels from around the world. And it also led many people to chance their luck – despite the researchers always pointing out that it was, statistically speaking, a very good way to lose money, as the winnings were in no way guaranteed to even cover the cost of the tickets.

Cushing says he has received numerous emails since the paper was released from people who cheerily announce that they have won tiny amounts, like two free lucky dips – essentially another free go on the lottery. “They were very happy to tell me how much they’d lost basically,” he says.

The pair did calculate that their method would have won them £1810 if they had played on one night during the writing of their research paper – 21 June. Both Cushing and Stewart had decided not to play the numbers themselves that night, but they have since found that a member of their research group “went rogue” and bought the right tickets – putting himself £1756 in profit.

“He said what convinced him to definitely put them on was that it was summer solstice. He said he had this feeling,” says Cushing, shaking his head as he speaks. “He’s a professional statistician. He is incredibly lucky with it; he claims he once found a lottery ticket in the street and it won £10.”

Cushing and Stewart say that while their winning colleague – who would prefer to remain nameless – has not even bought them lunch as a thank you for their efforts, he has continued to play the 27 lottery tickets. However, he now randomly permutes the tickets to alternative 27-ticket, guaranteed-win sets in case others have also been inspired by the set that was made public. Avoiding that set could avert a situation where a future jackpot win would be shared with dozens or even hundreds of mathematically-inclined players.

Stewart says there is no way to know how many people are doing the same because Camelot, which runs the lottery, doesn’t release that information. “If the jackpot comes up and it happens to match exactly one of the [set of] tickets and it gets split a thousand ways, that will be some indication,” he says.

Nonetheless, Cushing says that he no longer has any interest in playing the 27 tickets. “I came to the conclusion that whenever we were involved, they didn’t make any money, and then they made money when we decided not to put them on. That’s not very mathematical, but it seemed to be what was happening,” he says.

And Stewart is keen to stress that mathematics, no matter how neat a proof, can never make the UK lottery a wise investment. “If every single man, woman and child in the UK bought a separate ticket, we’d only have a quarter chance of someone winning the jackpot,” he says.

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*Credit for article given to Matthew Sparkes*

A mathematical game governed by simple rules throws up patterns of seemingly infinite complexity – and now a question that has puzzled hobbyists for decades has a solution.

A pattern in the Game of Life that repeats after every 19 steps

A long-standing mystery about repeating patterns in a two-dimensional mathematical game has been solved after more than 50 years with the discovery of two final pieces in the puzzle.

The result is believed to have no practical application whatsoever, but will satisfy the curiosity of the coterie of hobbyists obsessed with the Game of Life.

Invented by mathematician John Conway in 1970, the Game of Life is a cellular automaton – a simplistic world simulation that consists of a grid of “live” cells and “dead” cells. Players create a starting pattern as an input and the pattern is updated generation after generation according to simple rules.

A live cell with fewer than two neighbouring live cells is dead in the next generation; a live cell with two or three neighbouring live cells remains live; and a live cell with more than three neighbouring live cells dies. A dead cell with exactly three neighbouring live cells becomes live in the next generation. Otherwise, it remains dead.

These rules create evolving patterns of seemingly infinite complexity that throw up three types of shape: static objects that don’t change; “oscillators”, which form a repeating but stationary pattern; and “spaceships”, which repeat but also move across the grid.

One of the enduring problems in Game of Life research is whether there are oscillators with every “period”: ones that repeat every two steps, every three steps and so on, to infinity. There was a strong clue that this would be true when mathematician David Buckingham designed a technique that could create oscillators with any period above 57, but there were still missing oscillators for some smaller numbers.

Now, a team of hobbyists has filled those last remaining gaps by publishing a paper that describes oscillators with periods of 19 and 41 – the final missing shapes.

One member of the team, Mitchell Riley at New York University Abu Dhabi, works on the problem as a hobby alongside his research in a quantum computing group. He says there are lots of methods to generate new oscillators, but no way has been found to create them with specific periods, meaning that research in this area is a game of chance. “It’s just like playing darts – we’ve just never hit 19, and we’ve never hit 41,” he says.

Riley had been scouring lists of known shapes that consist of two parts, a hassler and a catalyst. Game of Life enthusiasts coined these terms for static shapes – catalysts – that contain a changing shape inside – a hassler. The interior reacts to the exterior, but leaves it unchanged, and together they form an oscillator of a certain period. Riley’s contribution was writing a computer program to discover potentially useful catalysts.

“The stars have to align,” he says. “You need the reaction in the middle to not destroy the thing on the outside, and the reaction in the middle, just by chance, to return to its original state in one of these new periods.”

Riley says that there are no applications known for this research and that he was drawn to the problem by “pure curiosity”.

Susan Stepney at the University of York, UK, says the work demonstrates some “extremely clever and creative techniques”, but it certainly isn’t the final conclusion of research on Conway’s creation.

“I don’t think work on Game of Life will ever be complete,” says Stepney. “The system is computationally universal, so there is always more behaviour to find, and it is seemingly so simple to describe, but so complex in its behaviour, that it remains fascinating to many.”

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*Credit for article given to Matthew Sparkes*

Researchers from Northwestern University, University of Pennsylvania, and University of Colorado published a new Journal of Marketing study that proposes abandoning null hypothesis significance testing (NHST) as the default approach to statistical analysis and reporting.

The study is titled “‘Statistical Significance’ and Statistical Reporting: Moving Beyond Binary” and is authored by Blakeley B. McShane, Eric T. Bradlow, John G. Lynch, Jr., and Robert J. Meyer.

Null hypothesis significance testing (NHST) is the default approach to statistical analysis and reporting in marketing and, more broadly, in the biomedical and social sciences. As practiced, NHST involves

1. assuming that the intervention under investigation has no effect along with other assumptions,
2. computing a statistical measure known as a P-value based on these assumptions, and
3. comparing the computed P-value to the arbitrary threshold value of 0.05.

If the P-value is less than 0.05, the effect is declared “statistically significant,” the assumption of no effect is rejected, and it is concluded that the intervention has an effect in the real world. If the P-value is above 0.05, the effect is declared “statistically nonsignificant,” the assumption of no effect is not rejected, and it is concluded that the intervention has no effect in the real world.

Criticisms of NHST

Despite its default role, NHST has long been criticized by both statisticians and applied researchers, including those within marketing. The most prominent criticisms relate to the dichotomization of results into “statistically significant” and “statistically nonsignificant.”

For example, authors, editors, and reviewers use “statistical (non)significance” as a filter to select which results to publish. Meyer says that “this creates a distorted literature because the effects of published interventions are biased upward in magnitude. It also encourages harmful research practices that yield results that attain so-called statistical significance.”

Lynch adds that “NHST has no basis because no intervention has precisely zero effect in the real world and small P-values and ‘statistical significance’ are guaranteed with sufficient sample sizes. Put differently, there is no need to reject a hypothesis of zero effect when it is already known to be false.”

Perhaps the most widespread abuse of statistics is to ascertain where some statistical measure such as a P-value stands relative to 0.05 and take it as a basis to declare “statistical (non)significance” and to make general and certain conclusions from a single study.

“Single studies are never definitive and thus can never demonstrate an effect or no effect. The aim of studies should be to report results in an unfiltered manner so that they can later be used to make more general conclusions based on cumulative evidence from multiple studies. NHST leads researchers to wrongly make general and certain conclusions and to wrongly filter results,” says Bradlow.

“P-values naturally vary a great deal from study to study,” explains McShane. As an example, a “statistically significant” original study with an observed P-value of p = 0.005 (far below the 0.05 threshold) and a “statistically nonsignificant” replication study with an observed P-value of p = 0.194 (far above the 0.05 threshold) are highly compatible with one another in the sense that the observed P-value, assuming no difference between them, is p= 0.289.

He adds that “however when viewed through the lens of ‘statistical (non)significance,’ these two studies appear categorically different and are thus in contradiction because they are categorized differently.”

Recommended changes to statistical analysis

The authors propose a major transition in statistical analysis and reporting. Specifically, they propose abandoning NHST—and the P-value thresholds intrinsic to it—as the default approach to statistical analysis and reporting. Their recommendations are as follows:

• “Statistical (non)significance” should never be used as a basis to make general and certain conclusions.
• “Statistical (non)significance” should also never be used as a filter to select which results to publish.
• Instead, all studies should be published in some form or another.
• Reporting should focus on quantifying study results via point and interval estimates. All of the values inside conventional interval estimates are at least reasonably compatible with the data given all of the assumptions used to compute them; therefore, it makes no sense to single out a specific value, such as the null value.
• General conclusions should be made based on the cumulative evidence from multiple studies.
• Studies need to treat P-values continuously and as just one factor among many—including prior evidence, the plausibility of mechanism, study design, data quality, and others that vary by research domain—that require joint consideration and holistic integration.
• Researchers must also respect the fact that such conclusions are necessarily tentative and subject to revision as new studies are conducted.

Decisions are seldom necessary in scientific reporting and are best left to end-users such as managers and clinicians when necessary.

In such cases, they should be made using a decision analysis that integrates the costs, benefits, and probabilities of all possible consequences via a loss function (which typically varies dramatically across stakeholders)—not via arbitrary thresholds applied to statistical summaries such as P-values (“statistical (non)significance”) which, outside of certain specialized applications such as industrial quality control, are insufficient for this purpose.

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Credit of the article given to American Marketing Association

 

Mathematicians have long been fascinated by the most efficient way of packing spheres in a space, and now physicists have confirmed that the best place to put them is into a sausage shape, at least for small numbers of balls.

Simulations show microscopic plastic balls within a cell membrane

What is the most space-efficient way to pack tennis balls or oranges? Mathematicians have studied this “sphere-packing” problem for centuries, but surprisingly little attention has been paid to replicating the results in the real world. Now, physical experiments involving microscopic plastic balls have confirmed what mathematicians had long suspected – with a small number of balls, it is best to stick them in a sausage.

Kepler was the first person to tackle sphere packing, suggesting in 1611 that a pyramid would be the best way to pack cannonballs for long voyages, but this answer was only fully proven by mathematicians in 2014.

This proof only considers the best way of arranging an infinite number of spheres, however. For finite sphere packings, simply placing the balls in a line, or sausage, is more efficient until there are around 56 spheres. At this point, the balls experience what mathematicians call the “sausage catastrophe” and something closer to pyramid packing becomes more efficient.

But what about back in the real world? Sphere-packing theories assume that the balls are perfectly hard and don’t attract or repel each other, but this is rarely true in real life – think of the squish of a tennis ball or an orange.

One exception is microscopic polystyrene balls, which are very hard and basically inert. Hanumantha Rao Vutukuri at the University of Twente in the Netherlands and his team, who were unaware of mathematical sphere-packing theories, were experimenting with inserting these balls into empty cell membranes and were surprised to find them forming sausages.

“One of my students observed a linear packing, but it was quite puzzling,” says Vutukuri. “We thought that there was some fluke, so he repeated it a couple of times and every time he observed similar results,” says Vutukuri. “I was wondering, ‘why is this happening?’ It’s a bit counterintuitive.”

After reading up on sphere packing, Vutukuri and his team decided to investigate and carried out simulations for different numbers of polystyrene balls in a bag. They then compared their predictions with experiments using up to nine real polystyrene balls that had been squeezed into cell membranes immersed in a liquid solution. They could then shrink-wrap the balls by changing the concentration of the solution, causing the membranes to tighten, and see what formation the balls settled in using a microscope.

“For up to nine spheres, we showed, both experimentally and in simulations, that the sausage is the best packed,” says team member Marjolein Dijkstra at Utrecht University, the Netherlands. With more than nine balls, the membrane became deformed by the pressure of the balls. The team ran simulations for up to 150 balls and reproduced the sausage catastrophe, where it suddenly becomes more efficient to pack things in polyhedrons, with between 56  and 70 balls.

The sausage formation for a small number of balls is unintuitive, says Erich Müller at Imperial College London, but makes sense because of the large surface area of the membrane with respect to the balls at low numbers. “When dimensions become really, really small, then the wall effects become very important,” he says.

The findings could have applications in drug delivery, such as how to most efficiently fit hard antibiotic molecules, like gold, inside cell-like membranes, but the work doesn’t obviously translate at this point, says Müller.

 

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*Credit for article given to Alex Wilkins*

Economics and physics are distinct fields of study, yet some researchers have been bridging the two together to tackle complex economics problems in innovative ways. This resulted in the establishment of an interdisciplinary research field, known as econophysics, which specializes in solving problems rooted in economics using physics theories and experimental methods.

Researchers at Kyoto University carried out an econophysics study aimed at studying financial market behaviour using a statistical physics framework, known as the Lillo, Mike, and Farmer (LMF) model. Their paper, published in Physical Review Letters, outlines the first quantitative validation of a key prediction of this physics model, which the team used to analyse microscopic data containing fluctuations in the Tokyo Stock Exchange market spanning over a period of nine years.

“If you observe the high-frequency financial data, you can find a slight predictability of the order signs regarding buy or sell market orders at a glance,” Kiyoshi Kanazawa, one of the researchers who carried out the study, told Phys.org.

“Lillo, Mike, and Farmer hypothetically modeled this appealing character in 2005, but the empirical validation of their model was absent due to a lack of large, microscopic datasets. We decided to solve this long-standing problem in econophysics by analysing large, microscopic data.”

The LMF model is a simple statistical physics model that describes so-called order-splitting behaviour. A key prediction of this model is that the order of signs representing buy or sell orders in the stock market is associated with the microscopic distribution of metaorders.

This hypothesis has been largely debated within the field of econophysics. So far, validating it was unfeasible, as it required large microscopic datasets representing financial market behaviour over the course of several years and with high resolution.

“The first key aspect of our study is that we used a large, microscopic dataset of the Tokyo Stock Exchange,” Kanazawa said. “Without such a unique dataset, it is challenging to validate the LMF model’s hypothesis. The second key point for us was to remove the statistical bias due to the long-memory character of the market-order flow. While statistical estimation is challenging regarding long-memory processes, we did our best to remove such biases using computational statistical methods.”

Kanazawa and his colleagues were the first to perform a quantitative test of the LMF model on a large microscopic financial market dataset. Notably, the results of their analyses were aligned with this model’s predictions, thus highlighting its promise for tackling economic problems and studying the financial market’s microstructure.

“Our work shows that the long memory in the market-order flows has microscopic information about the latent market demand, which might be used for designing new metrics for liquidity measurements,” Kanazawa said.

“We showed that the quantitative power of statistical physics in clarifying financial market behaviour with large, microscopic datasets. By analysing this microscopic dataset further, we would now like to establish a unifying theory of financial market microstructure parallel to the statistical physics programs from microscopic dynamics.”

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Credit of the article given to Ingrid Fadelli , Phys.org

When middle school math teachers completed an online professional development program that uses artificial intelligence to improve their math knowledge and teaching skills, their students’ math performance improved.

My colleagues and I developed this online professional development program, which relies on a virtual facilitator that can—among other things—present problems to the teacher around teaching math and provide feedback on the teacher’s answers.

Our goal was to enhance teachers’ mastery of knowledge and skills required to teach math effectively. These include understanding why the mathematical rules and procedures taught in school work. The program also focuses on common struggles students have as they learn a particular math concept and how to use instructional tools and strategies to help them overcome these struggles.

We then conducted an experiment in which 53 middle school math teachers were randomly assigned to either this AI-based professional development or no additional training. On average, teachers spent 11 hours to complete the program. We then gave 1,727 of their students a math test. While students of these two groups of teachers started off with no difference in their math performance, the students taught by teachers who completed the program increased their mathematics performance by 0.18 of a standard deviation more on average. This is a statistically significant gain that is equal to the average math performance difference between sixth and seventh graders in the study.

Why it matters

This study demonstrates the potential for using AI technologies to create effective, widely accessible professional development for teachers. This is important because teachers often have limited access to high-quality professional development programs to improve their knowledge and teaching skills. Time conflicts or living in rural areas that are far from in-person professional development programs can prevent teachers from receiving the support they need.

Additionally, many existing in-person professional development programs for teachers have been shown to enhance participants’ teaching knowledge and practices but to have little impact on student achievement.

Effective professional development programs include opportunities for teachers to solve problems, analyse students’ work and observe teaching practices. Teachers also receive real-time support from the program facilitators. This is often a challenge for asynchronous online programs.

Our program addresses the limitations of asynchronous programs because the AI-supported virtual facilitator acts as a human instructor. It gives teachers authentic teaching activities to work on, asks questions to gauge their understanding and provides real-time feedback and guidance.

What’s next

Advancements in AI technologies will allow researchers to develop more interactive, personalized learning environments for teachers. For example, the language processing systems used in generative AI programs such as ChatGPT can improve the ability of these programs to analyse teachers’ responses more accurately and provide more personalized learning opportunities. Also, AI technologies can be used to develop new learning materials so that programs similar to ours can be developed faster.

More importantly, AI-based professional development programs can collect rich, real-time interaction data. Such data makes it possible to investigate how learning from professional development occurs and therefore how programs can be made more effective. Despite billions of dollars being spent each year on professional development for teachers, research suggests that how teachers learn through professional development is not yet well understood.

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Credit of the article given to Yasemin Copur-Gencturk, The Conversation

 

The simple activity of walking through a room jumpstarts the neurons in the human brain. An explosion of electrochemical events or “neuronal spikes” appears at various times during the action. These spikes in activity, otherwise known as action potentials, are electrical impulses that occur when neurons communicate with one another.

Researchers have long thought that spike rates are connected to behaviour and memory. When an animal moves through a corridor, neuronal spikes occur in the hippocampus—an area of the brain involved in memory formation—in a manner resembling a GPS map. However, the timing in which these spikes happen and their connection to events in real-time, was thought of as random until it was discovered that these spikes happen with a specific and precise pattern.

Developing a new approach to studying this phenomenon, Western University neuroscientists are now able to analyse the timing of neuronal spikes. Their research found that spike timing may be just as important as spike rate for behaviour and memory.

“More and more experimental evidence is accumulating for the importance of spike times in sensory, motor, and cognitive systems,” said Lyle Muller, senior author of the paper and assistant professor in the Faculty of Science.

“Yet, the exact computations that are being done through spike times remain unclear. One reason for this may be that there isn’t a clear mathematical language for talking about spike-time patterns across neurons—which is what we set out to develop.”

Published recently in the journal Physical Review E, the paper outlines a new mathematical technique to study the neural codes taking place during spike-time sequences.

“Neurons fire at really specific times with respect to an ‘internal clock,’ and we wanted to know why,” said Alex Busch, co-first author of the paper and a Western BrainsCAN Scholar. “If neurons are already keeping track of the animal’s position through spike rates, why do we need to have specific times on top of that? What additional information does that provide?”

Busch, along with co-first author Federico Pasini, assistant professor in the department of mathematics at Huron College, identified spike times from known experimental data. Studying the patterns as a code, the researchers were able to transfer the spike times into a mathematical equation.

“This is the first time we are able to ask what computation could be done with these spike times. What we found was that it’s more than just current location; the pattern of spike times actually creates a link between the recent past and future predictions that’s encoded in the timing of spikes itself,” said Busch, a Ph.D. student in the department of mathematics now working to create new mathematical approaches to analyse and understand spike times. “These are the sorts of patterns that may be important for learning and memory.”

Beyond giving researchers a method to study spike times and their relation to behaviour and memory, this study also paves the way for studying deficits found in neurodegenerative diseases. A better understanding of the significance of spike times may lead to a better understanding of what happens when spike patterns break down in Alzheimer’s disease and other memory disorders.

“If we have a language for spike times, we can understand the computations that might be occurring. If we can understand the computations, we can understand how they break down and suggest new techniques to fix them,” said Muller.

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Credit of the article given to Maggie MacLellan, University of Western Ontario

A new Sussex study has revealed that “math anxiety” can lead to disengagement and create significant barriers to learning. According to charity National Numeracy, more than one-third of adults in the U.K. report feeling worried or stressed when faced with math, a condition known as math anxiety.

The new paper, titled “Understanding mathematics anxiety: loss aversion and student engagement” and published in Teaching Mathematics and its Applications finds that teaching which relies on negative framing, such as punishing students for failure, or humiliating them for being disengaged, is more likely to exacerbate math anxiety and disengagement.

The paper says that in order to successfully engage students in math, educators and parents must build a safe environment for trial and error and allow students space to make mistakes and stop learners from reaching the point where the threat of failure becomes debilitating.

Author Dr. C. Rashaad Shabab, Reader in Economics at the University of Sussex Business School, said, “As the government seeks to implement universal math education throughout higher secondary school, potentially a million more people will be required to study math who might otherwise have chosen not to.

“The results of this study deliver important guiding principles and interventions to educators and parents alike who face the prospect of teaching math to children who might be a little scared of it and so are at heightened risk of developing mathematics anxiety.

“Teachers should tell students to look at math as a puzzle, or a game. If we put a piece of a puzzle in the wrong place, we just pick it up and try again. That’s how math should feel. Students should be told that it’s okay to get it wrong, and in fact that getting it wrong is part of how we learn math. They should be encouraged to track their own improvement over time, rather than comparing their achievements with other classmates.

“All of these interventions, basically take the ‘sting’ out of getting it wrong, and it’s the fear of that ‘sting’ that keeps students from disengaging. The findings could pave the way for tailored interventions to support students who find themselves overwhelmed by the fear of failure.”

Using behavioural economics, which combines elements of economics and psychology to understand how and why people behave the way they do, the research, from the University of Sussex’s Business School, identifies math anxiety as a reason why even dedicated students can become disengaged. This often results in significant barriers to learning, both for the individual in question and others in the classroom.

The paper goes on to say that modern technology and elements of video game design can help those struggling with mathematics anxiety through a technique called “dynamic difficulty adjustment.” This would allow the development of specialist mathematics education computer programs to match the difficulty of math exercises to the ability of each student. Such a technique, if adopted, would keep the problems simple enough to avoid triggering anxiety, but challenging enough to improve learning.

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Credit of the article given to Tom Walters, University of Sussex

 

In a new study published in The Journal of Finance and Data Science, a researcher from the International School of Business at HAN University of Applied Sciences in the Netherlands introduced the topological tail dependence theory—a new methodology for predicting stock market volatility in times of turbulence.

“The research bridges the gap between the abstract field of topology and the practical world of finance. What’s truly exciting is that this merger has provided us with a powerful tool to better understand and predict stock market behaviour during turbulent times,” said Hugo Gobato Souto, sole author of the study.

Through empirical tests, Souto demonstrated that the incorporation of persistent homology (PH) information significantly enhances the accuracy of non-linear and neural network models in forecasting stock market volatility during turbulent periods.

“These findings signal a significant shift in the world of financial forecasting, offering more reliable tools for investors, financial institutions and economists,” added Souto.

Notably, the approach sidesteps the barrier of dimensionality, making it particularly useful for detecting complex correlations and nonlinear patterns that often elude conventional methods.

“It was fascinating to observe the consistent improvements in forecasting accuracy, particularly during the 2020 crisis,” said Souto.

The findings are not confined to one specific type of model. It spans across various models, from linear to non-linear, and even advanced neural network models. These findings open the door to improved financial forecasting across the board.

“The findings confirm the theory’s validity and encourage the scientific community to delve deeper into this exciting new intersection of mathematics and finance,” concluded Souto.

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Credit of the article given to KeAi Communications Co.