Hello and welcome to Crowdscience from the BBC World Service. I’m Anand Jagatia and as you can hear we’re currently surrounded by livestock. I want to see if you can work out how many of each animal there are.
To give you some help, here’s the farmer: Well, I only keep sheep, goats and horses. In fact, at the moment they are all sheep bar three, all goats bar four and all horses bar five. I have to admit that’s a tricky one.
And I also have to admit that this isn’t a show about farming, it’s a show about maths and numbers. Now I did spring that on you, so in case you missed it, here’s the farmer’s question one more time. Fine, I’ll repeat it then.
Get a pencil to write it down if it helps, I’ll wait. At the moment, my animals are all sheep except three, all goats except four and all horses except five. How many of each do I have?
I'll reveal the solution at the end of the show but how did you find that? Did you manage to get to the answer already? Does working with numbers fill you with dread?
Or does it come easily to you? Well, it definitely doesn’t come easily to our listener Israel from Papua New Guinea, who got in touch with this week’s question. My question to CrowdScience is, why am I really bad in math?
And why are others better than me in math? I've been very bad in math since the third grade or something. Do you have like a memory of a time, maybe when you were in third grade, of how you found maths hard?
Or in what way you struggled with math? Yeah I can remember this one time. The teacher taught us long division throughout the week.
And at the end of the week, she gave a test. Most people did better in the test. So I asked my friend, 'how come you got better marks in math in long division and I didn't?
' And he just said, 'well, you're just naturally slow in math'. Yeah. It's interesting, isn't it?
Because for some people, even if they study hard and they work hard, there's just something about maths that they just really find difficult. Was that your experience? Yeah.
I tried studying hard, memorising the multiplication, times table and doing more activities, doing the same activities that other people who are good in math did, but still I didn't get as good as they were. Yeah, I kind of hated that subject towards the end. Thanks Israel for getting in touch.
So why are some people better with numbers than others? Maths is one of those subjects that tends to divide the crowd and also, it turns out, CrowdScience listeners. We reached out and asked you to tell us about your relationship with mathematics: Hello.
Hi CrowdScience. This is my little maths story. Some of you felt you were bad at maths.
. . Everything looked complicated and even questions I was able to solve before now looked like hieroglyphics.
Some of you excelled. . .
Things finally clicked. Geometry? Tick.
Trigonometry? Tick. Calculus?
That's easy. Some of you noticed clear differences between your classmates. .
. There were always a group of people who were able to come up with some creative solutions to difficult maths problems. Some, like Israel, didn't enjoy it very much.
. . So maths, wow, not so good memories.
While some of you loved it at school. . .
It's like this mysterious puzzle that I can't help but want to solve. Mathematics has always evoked mixed emotions within me. I see mathematics as a language.
I think we're traumatising our children for no good reason. Until I had a new teacher. I don't know how to calculate them.
So you just do it. And I am now a maths teacher. Always hated math.
Undefined. Pure euphoria. Thanks to everyone who got in touch with us.
So clearly listener Israel isn’t alone in thinking about this stuff and one thing he mentioned was that his classmate told him he was 'naturally slow' at maths. But what does that really mean? And is it true that some people can be 'naturally' good or bad at maths?
It's a very good question. And often, when people talk about naturally being good or bad, naturally at something, they also refer to some concept of being born with something. This is Professor Yulia Kovas from Goldsmiths University of London.
She’s a geneticist and a psychologist who studies why people have different mathematical abilities. I often hear kind of very deterministic views about genetics that, let's say, I'm bad at maths because everyone in my family is bad at maths. So it's genetics and nothing can be done about it.
Similarly, there are examples of for example mathematical talent running in families, that people often think that that means it's not malleable in any way. But all of these assumptions are wrong, because mathematical talent or disability may run in families for both genetic and environmental reasons. Okay.
So I guess, you know, your job as someone who's researching this is to try and untangle these factors. How would you go about studying that and what some of the work that you've done in that space? I've worked for many years on a on a very large scale twin study in the UK, which has about 10,000 pairs of twins consistently followed from birth.
And so in the study we compare identical and non-identical twins. And one more thing is all twins live in the same families. So here you have a perfect kind of control for environmental factors.
They all live together. They have the same family, the same parents, same socioeconomic status. So a lot of factors equalised.
But identical twins, they are more similar than non-identical twins on every psychological characteristic we studied. So they're more similar in mathematical ability. And that suggests that home environments do not explain all the variability, it seems that genes do contribute.
Right. Okay. So because the identical twins and the non-identical twins have both pretty much had as similar life as it is possible to live, but the identical twins who are exactly the same genetically are more similar, you can say, well, there's got to be something going on here with the genes.
That's That's right. So this is a kind of usual conclusion from twin studies. And the evidence is quite solid.
Okay, so I guess we can say that there's good evidence that there is some genetic or kind of inherited component to like how whether you're good or bad at math. But how much of a big deal is that? Well, if we look at the estimates, it seems that in secondary school and in adulthood, the heritability, genetic component of mathematical learning and ability is about 50 to 60%.
So it's an interesting kind of number. It reinforces this idea that genes and environments are both important, and to a similar extent, in a way. We know now that genes and environments always co-act, so they kind of interactively affect our characteristics, but I think what is very important to mention that when we talk about environments we don't mean something very specific like teachers or parents or schools or something.
That there are really thousands of factors that can be in play and of particular importance are environments that are not systematic, that are kind of individual- specific, maybe random, you know, maybe something you heard on the radio may change the whole path of your interest or motivation, it's unpredictable and random. I mean the word environment, we're using it in quite a scientific sense there. But maybe it would be more accurate to describe it as everything your body has ever experienced.
Yes. And then that would sort of give people a sense of like just how broad it can be. And like you say, suddenly can send you on a path that you would never be able to trace and never be able to know, but that's just what life is like.
And there is a concept for this recently kind of discussed in the literature. It's called exposome. Ex, you know, things you're exposed to throughout your life.
So you have your genome and your exposome as well. Your collection of everything. But even these, like genome and exposome, are not unrelated because in many ways your genetic propensities may lead you towards particular exposures.
And even if both of us hear the same radio programme, we can extract completely different things from it. So exposome is kind of subjective. I find Yulia’s research kind of surprising.
Our genes do seem to play a significant role in how good we are at maths. But that’s not to say that there’s a single 'maths gene' and it’s also not the whole picture. Our environment, or 'exposome', also has a huge influence.
Perhaps this episode of CrowdScience will have a bearing on your future mathematical ability. Although, as ever, more research is needed. But if, like listener Israel, you think you’re bad at maths, perhaps if you’re studying it currently at school, this doesn’t help you very much.
You can’t control your genes and it’s not always easy to change your environment. So do we, as individuals, have any control over how good we are with numbers? Is it possible to change your mathematical fate?
Thank you so much for asking that question because we need to set the record straight here. Iro Xenidou-Dervou is a researcher at Loughborough University in the UK in the department of mathematics education. Everybody I feel needs to know that we can all improve in mathematics.
We might not all become, you know, expert mathematicians. But we can all develop the numeracy and mathematical skills that can help us thrive and improve our quality of life. We must not forget that there is also a lot of evidence, both from us but from many other colleagues around the world, showing how our thoughts, our beliefs, our attitudes, our emotions around mathematics, that includes mathematics anxiety, influence our maths learning journey and our performance.
So it's important for people who want to improve their maths skills to also believe that they can. It needs time and effort, like anything in life, right? I wanted to pick up on something you mentioned there around emotion and how you feel about maths and belief.
So this is something that our listener Israel mentioned. When he was doing maths at school he struggled with it initially. And he did badly on a test.
And then he started to really hate the subject. What do we know about the things that can affect them, or make their journey even more difficult or worse? Yeah, so feelings and emotions and beliefs and attitudes play a very important role.
If at any point, for example, you fall behind for a bit, or you're exposed to also gender stereotypes, or you have negative experiences like your listener regarding maths, it can be at home or at school, you might start developing anxious thoughts and feelings around maths that kind of start a vicious circle. So anxiety in maths leads to avoidance of maths, which also then leads to poor performance, which then increases maths anxiety even further. What maths anxiety does is that it overloads our working memory.
Working memory is the mental space where our thinking takes place. It is where information is stored and processed for a very brief amount of time and it's very, very limited. So what happens with anxiety is that these negative anxious thoughts take up a lot of this precious space in our working memory and there's very little left for you to actually use to solve the problem at hand.
We've recently conducted a study at Loughborough with my team where we looked at this link between working memory and maths anxiety and children's mental arithmetic. These were children nine to 10 years of age and they did a two digit mental arithmetic task on its own, but also in a condition where we interfered with their working memory. So that is they heard words before the arithmetic problem.
And then they had to recall these words verbally, so they had to retain them while doing the arithmetic task. And what we found is that of course the working memory load impaired impacted children's performance, but we found that this was particularly crucial for highly maths anxious children. For them, they were not doing two tasks, they were actually doing three tasks.
It really amplified the effect for high maths anxious children. What I'm really curious about is like, what is it about maths that's different from history that it means. .
. because, you know, people don't talk about having history anxiety. What is it about maths that it means it has this kind of power over people?
Probably it's the fact that it entails so many skills that are that are so intertwined, right? Maths is complex. I also view maths learning as building a mental brick wall, you need to set all these bricks, right to set those solid foundations.
You can't really skip bricks in the mathematics domain. For example, in history, perhaps you don't know very well one particular era and that's fine. But in mathematics, you really can't do that.
You need to build those solid foundations to later on be able to advance to more higher order mathematics. Is there practical advice that you can offer to people who might struggle with maths or feel badly about it and want to change their relationship with it? Absolutely.
I want your listeners to know it's never too late to learn maths and improve your numeracy skills. You have to believe that you can do it. It takes time and effort, but there are many resources online that can help you achieve that goal.
Be kind to yourself. You want to try to change your mindset, you have to believe that you can do this and slowly start strengthening your numerical mathematical skills. You’re listening to CrowdScience from the BBC World Service, where we’re answering a question from listener Israel, who wants to know why he’s bad at maths.
So far we’ve heard that part of the answer is in our genes. But that doesn’t mean your success in maths is set from birth. Just as important are all the things out there in the world that shape us over the course of our lives.
And no matter how much you might struggle, all of us can improve our skill with numbers. While it’s helpful to know that we can get better at maths if we believe that we can, the right attitude can only take you so far. As children, the way that we are taught maths in school is surely an important part of the puzzle.
And that depends on where you are in the world. So I went back to Professor Yulia Kovas to ask if there are any countries where maths education is particularly strong and she told me about some interesting findings from the early 2000s. At the top of the international rankings were Chinese students, some other countries, East Asian countries, and Finland.
And so Finland has been branded as a kind of European paradox because it's there amongst these other East Asian countries. Yulia is talking about something called the PISA survey, which, among other things, tests basic maths skills in 15 year olds from various countries. Rankings like this aren’t perfect and there are limits to what they can tell us.
Just because you do well on a standardised test doesn’t necessarily mean that your education system is better. But in 2003, Finland surprised a lot of people by getting remarkably good results. So is there anything we can learn from countries that tend to perform well?
I called up to two education experts to find out. My name is Zhenzhen Miao. I'm currently assistant professor at Jiangxi Normal University in China.
My name is Pekka Räsänen, I work as a professor of practice at the University of Turku in Finland. One thing that both of these countries have in common is that they focus on the basics when it comes to maths. The main philosophy in the Finnish education system used to be guarantee the basic skills for all.
The four basics, which is about the basic knowledge, basic skills, basic masking experiences and basic mathematical thinking. And another is that teachers are well supported and respected. So all the teachers in Finland get five years academic training.
And because of the respect the teachers have. It's a profession want youngsters want to have. So we have 10 times more applicants than we have study positions.
Yeah, teachers are well respected, well regarded and education is also well regarded. Yeah, in comparison with other professions, I think they are well paid. So we have very highly qualified teachers, who also at the work have a lot of freedom to do their work the way they want to do.
They will only need to teach one to two lessons a day and the rest of the time they will be able to talk to their peers to discuss and plan lesson together and give each other advice on how to improve that specific lesson. But there are also differences, including how well the best and the worst students do in each country. Here’s Yulia again.
If you look at the variability within countries, let's say in China, does everybody do well? Well, no, there is a huge variability like in every other country. And the difference between worst performing and best performing children translates into like 10 years of schooling.
It's as if one never went to school and one has already completed 10 years of education, which just demonstrates the complexity. And if you look at the Finnish kind of distribution, what they're showing is that at the top, Finnish children perform very similarly to top performers in other countries. But at the bottom, there are fewer children who are doing really badly.
And so in that sense, on average, they're doing better. So if they're putting efforts into helping struggling children not to do really badly, then that's already a huge thing. Were the top performers are now more brilliant at maths?
Time will show probably not. So you could say that Finland has some of the best worst maths students. So how do they do it?
I asked Finnish education expert Pekka. The high levels of investment to special support for learning. So every school has special teachers who do not have their own classroom, but they are teaching those kids who are falling behind in education.
And they are trying to guarantee that everyone will learn the basics in mathematics. I should point out that in recent years, Finland has dropped down the rankings to be more in line with other European nations. Although it’s still number 13 out of 81 countries tested.
it's still number 13 out of 81 countries tested. It’s unlikely that there’s a secret formula for brilliant maths education. Instead it’s more about things like persevering with the foundations and making sure teachers can do their jobs properly.
No surprises there. It's also really hard to compare different teaching systems given cultural and societal differences between countries. There's this nice saying about when you're trying to explain a very complex systemic phenomena, there is an answer, which is simple, neat and wrong.
Exactly. We humans tend to like answers that are simple and neat, aren't they? Yeah, there's never an answer, we cheat, which is just one factor affecting things.
So far we’ve looked at genes, emotions, education and environment. But there’s one last thing we have to explore in some people that struggle with maths. To understand what that is, we have to look at how we sense quantity.
And we might get some clues from cultures that don’t have words for numbers. Cultures which are non-numerate, where the languages contain no counting words, not even words for how many. Brian Butterworth is a Professor at University College London who has studied counting in indigenous communities in Australia.
They have markers on some of their nouns and verbs about whether it's all or some or few, right, they don't have words or markers for specific numbers like one, two, three or four. I guess they don't need them? Like they get on fine without them?
They get on fine without them. So for example, they're when they're trading, which they do often across long distances, it's face to face trading, I'll give you this if you give me that. Then on the whole hunter gatherers, so they don't have flocks to tend.
And when they gather, they just gather what's there and take it back to their camp. So you looked at a specific community who have one of these languages, whereabouts in Australia do they live? Actually we looked at two different communities, one in the central desert, a few hundred kilometres from Alice Springs and another on an island off the north coast of Australia.
So we could test two separate communities to see what monolingual children in those communities could do with numbers. Now, it's quite difficult because you can't ask them how many nuts are on a tray? You literally can't ask them because there are no words to answer that question.
You can't ask them. But you can do this kind of test, which is you put out a number of nuts on your tray. And you say make your trade the same as my tray.
We can also test things like addition. So I put, let's say, four nuts on my tray, cover them up and then in full view of the child put, let's say, another three nuts under the cover and say right now make your tray like my tray. And so if they've done the addition in their heads, they'll put out seven nuts on their tray.
And they can do this. Wow. So with these kids, is it just a visual thing?
Does it only work if they can see you putting the nuts out or can they go to more abstract levels than that? Well, numbers are abstract. So in order for them really to have numbers you have to test whether they actually have an abstract sense of number.
So we did another test, which is we took two sticks. This is very high tech research. And we would bang the sticks several times.
Let's say we would bang four times. And the learner had to put out the same number of counters on a mat that corresponded to the number of bangs. They clearly have the concept so they could do it.
Brian’s work shows that humans have a built in sense for numbers. Even children that have never been taught to count, because they literally don’t have the language for it, have this sense. But the important thing for Israel’s question is that in some people, this sense doesn’t seem to work very well.
Yes, some people have very bad numerical sense, and very easy to test, because the innate mechanism is designed to extract numerical information from the environment. So you can test individual number sense by asking them to do a task like say how many dots there are on the screen and you can look at how accurate they are at that and how quick they are at that so you could create a measure of their efficiency in extracting numerical information from the environment. And individuals who are not very good at this tend to have great deal of trouble learning ordinary arithmetic - things that you and I can do rather easily they find extremely difficult.
And we call these people dyscalculics and so we explain to them and this they find helpful that the reason they can't learn basic arithmetic is not because they're stupid and not because their teachers are very bad, it's because their innate mechanism doesn't work very well. So it's actually quite easy to distinguish individuals who are bad at arithmetic because they have this problem from those who are bad at arithmetic for a whole range of other reasons like their parents haven't helped them early on, their teachers have given them inappropriate instruction or because they're very hungry or because they don't have a school to go to. These are all reasons why you're bad at arithmetic.
And I mean, how common is it? So I'm sure most people have heard of dyslexia, but maybe dyscalculia is less known about so yeah. How prevalent is this condition?
We think it's about as prevalent as dyslexia properly diagnosed, so it's about 5%. People with dyscalculia tend to struggle even with simple arithmetic tasks, like 5x8, or 6+16. But Brian and his team have developed something that might help.
We've run tests on this game, because. . .
Can we have a look at this game? Yes sure go to the first level, breaking and breaking one. There's a full introduction.
On the screen there have lines of beads in groups of up to 10. Each amount has a different colour and sets can be combined or you can split them. Okay so I'll cut this four into two sets of two.
The idea is to build or break these sets of beads to produce a target amount and this helps children understand that five beads, for example, contains a set of two and a three. Exactly. And to get them to represent numerical information in terms of sets.
Until you get to later levels. You get on to the next level. Where you're learning to associate these beads with the digits.
At the end. . .
okay, so this level now there are no beads, there are no beads at all. There are just the digits. Brian has run tests using this game in London, Italy and Singapore and found that it helps children with basic arithmetic, in particular those with dyscalculia.
But it's still unclear what interventions like this could do in the long term. We can help kids and adults have a better understanding of how numbers work. Whether there'll ever be fluent calculators like you are Anand or I am is not clear.
Because what you would need to do is intervene early and then track the development of these kids over the next few years. Start in year one and end up say in year five or year six and see if it really does cure them or whether it helps them be a little bit more competent. So, listener Israel, you asked us: Why am I bad at maths?
We’ve heard that there are many factors at play here - including your genes, environmental factors, the place you learned mathematics. . .
I remember going to school in China. . .
as well as your motivation and emotions when it comes to numbers. . .
The anxiety I have about math. But there is hope. If maths is important to you and you want to improve, you can get better.
. . I shut myself in a room with a book.
. . Although it might be hard work, which is like anything.
. . And then I aced that final test too.
There are some people however - likely around 5% - that have a learning disorder which affects their number sense. Which does make it a lot harder to learn arithmetic, things like 5+8 or 10x15. But there is much more to maths than sums.
So to end the show, let me introduce you to Emma. She doesn’t have an official dyscalculia diagnosis, but has always struggled with numbers and has gone on to do great things. I studied astrophysics at University and I did a PhD in cosmology, which are both very mathematical subjects, I'm also really, really bad at mental arithmetic.
At school I never managed to learn my times tables and I still can't work out the offers in a supermarket without a calculator. Despite this I was always quite good at what people tend to consider to be more advanced types of mathematics, things like algebra or calculus but of course that doesn't mean that you can't get good at things that you find difficult. I did actually learn my times tables as an adult because I needed them to pass a test and I was very very motivated to pass that test.
Of course I've forgotten them again now but at least I know it's not actually impossible just that for me that's a lot of hard work. Thanks Emma. And just before I go, as promised, the answer to the problem at the start of the show.
Remember my question? All my animals are sheep except three or goats except four and all horses except five, how many of each animal do I have? The answer is one horse, two goats and three sheep.
That's correct. Now this is a bit of a tricky one, so if you didn't get the answer here is one way of working it out. So all of my animals are sheep except three means that horses and goats must equal three, so there could be one horse and two goats or two goats and one horse.
But we know that they are all goats except four and that they are all horses except five, which means that there must be more goats than horses. So that means that there is one horse and two goats. But we also know that all of them horses except five.
So five animals minus two goats equals three sheep. And that's it. Well done if you got the answer, you clever thing.
Now back to listener to Israel for the credits. That's it for this episode of CrowdScience from the BBC World Service. It was presented by Anand Jagatia and produced by Florian Bohr.
Today's question came from me Israel in Port Moresby, Papua New Guinea. If you have a science question you'd like the CrowdScience team to look into, you can do what I did and email crowdscience@bbc. co.
uk. Thank you very much for listening, bye.
