Blind people use brain’s visual cortex to help do maths

From New Scientist, by Colin Barras, September 2016:

“It’s actually hard to think of a situation when you might process numbers through any modality other than vision,” says Shipra Kanjlia at Johns Hopkins University in Baltimore, Maryland.

But blind people can do maths too. To understand how they might compensate for their lack of visual experience, Kanjlia and her colleagues asked 36 volunteers – 17 of whom had been blind at birth – to do simple mental arithmetic inside an fMRI scanner. To level the playing field, the sighted participants wore blindfolds.

We know that a region of the brain called the intraparietal sulcus (IPS) is particularly active when sighted people process numbers, and brain scans revealed that the same area is similarly active in blind people too.

“It’s really surprising,” says Kanjlia. “It turns out brain activity is remarkably similar, at least in terms of classic number processing.”

Read the whole story. Journal reference: PNAS, DOI: 10.1073/pnas.1524982113

From the original research paper:

Significance

Human numerical reasoning relies on a cortical network that includes frontal and parietal regions. We asked how the neural basis of numerical reasoning is shaped by experience by comparing congenitally blind and sighted individuals. Participants performed auditory math and language tasks while undergoing fMRI. Both groups activated frontoparietal number regions during the math task, suggesting that some aspects of the neural basis of numerical cognition develop independently of visual experience. However, blind participants additionally recruited early visual cortices that, in sighted populations, perform visual processing. In blindness, these “visual” areas showed sensitivity to mathematical difficulty. These results suggest that experience can radically change the neural basis of numerical thinking. Hence, human cortex has a broad computational capacity early in development.

Abstract

In humans, the ability to reason about mathematical quantities depends on a frontoparietal network that includes the intraparietal sulcus (IPS). How do nature and nurture give rise to the neurobiology of numerical cognition? We asked how visual experience shapes the neural basis of numerical thinking by studying numerical cognition in congenitally blind individuals. Blind (n = 17) and blindfolded sighted (n = 19) participants solved math equations that varied in difficulty (e.g., 27 − 12 = x vs. 7 − 2 = x), and performed a control sentence comprehension task while undergoing fMRI. Whole-cortex analyses revealed that in both blind and sighted participants, the IPS and dorsolateral prefrontal cortices were more active during the math task than the language task, and activity in the IPS increased parametrically with equation difficulty. Thus, the classic frontoparietal number network is preserved in the total absence of visual experience. However, surprisingly, blind but not sighted individuals additionally recruited a subset of early visual areas during symbolic math calculation. The functional profile of these “visual” regions was identical to that of the IPS in blind but not sighted individuals. Furthermore, in blindness, number-responsive visual cortices exhibited increased functional connectivity with prefrontal and IPS regions that process numbers. We conclude that the frontoparietal number network develops independently of visual experience. In blindness, this number network colonizes parts of deafferented visual cortex. These results suggest that human cortex is highly functionally flexible early in life, and point to frontoparietal input as a mechanism of cross-modal plasticity in blindness.

Olivier Gerard: Learning mathematics as a Russian interpreter

You might be interested in reading How I Rewired My Brain to Become Fluent in Math, by Barbara Oakley, in Nautilus, October 2, 2014.

A quote:

“Time after time, professors in mathematics and the sciences have told me that building well-ingrained chunks of expertise through practice and repetition was absolutely vital to their success. Understanding doesn’t build fluency; instead, fluency builds understanding. In fact, I believe that true understanding of a complex subject comes only from fluency.

In other words, in science and math education in particular, it’s easy to slip into teaching methods that emphasize understanding and that avoid the sometimes painful repetition and practice that underlie fluency. “

How to raise a genius: lessons from a 45-year study of super-smart children

How to raise a genius: lessons from a 45-year study of super-smart children, by Tom Clynes, 07 September 2016, in Nature | News Feature.

On a summer day in 1968, professor Julian Stanley met a brilliant but bored 12-year-old named Joseph Bates. The Baltimore student was so far ahead of his classmates in mathematics that his parents had arranged for him to take a computer-science course at Johns Hopkins University, where Stanley taught. Even that wasn’t enough. Having leapfrogged ahead of the adults in the class, the child kept himself busy by teaching the FORTRAN programming language to graduate students.

Unsure of what to do with Bates, his computer instructor introduced him to Stanley, a researcher well known for his work in psychometrics — the study of cognitive performance. To discover more about the young prodigy’s talent, Stanley gave Bates a battery of tests that included the SAT college-admissions exam, normally taken by university-bound 16- to 18-year-olds in the United States.

Read the rest of the story

The 7 biggest problems facing science

The 7 biggest problems facing science, according to 270 scientists, by Julia Belluz, Brad Plumer, and Brian Resnick on September 7, 2016 in Vox.

I love this example of deductive resoning:

  •  Academia has a huge money problem
  • Too many studies are poorly designed
  • Replicating results is crucial — and rare
  • Peer review is broken
  • Too much science is locked behind paywalls
  • Science is poorly communicated
  • Life as a young academic is incredibly stressful

Conclusion:

  • Science is not doomed

Read the whole text.

Benefits of Asian-style maths teaching

You may import a “style of teaching”, but cannot import the social environment of teaching — this is a key, and, perhaps, impassible obstacle to development of a coherent mathematics education policy in England. But attempts continue regardless: DfE has no other options.

From BBC:

Thousands of primary schools in England are to be offered the chance to follow an Asian style of teaching maths.

More from BBC:

Asian maths method offered to schools

The government is providing £41m of funding to help interested schools to adopt this method, which is used in high performing places like Shanghai, Singapore and Hong Kong.

The money will be available to more than 8,000 primary schools in England.

This approach to maths is already used in some schools, but the cash means it can be taken up more widely.

The Department for Education says the mastery approach to maths teaching, as it is known, involves children being taught as a whole class and is supported by the use of high-quality textbooks.

Read the full story.  Coming soon: comments on mastery and NCETM‘s thinking

More detailed explanations of the NCETM’s thinking in this developing area can be found in several posts on the blog page of our Director, Charlie Stripp, in a document entitled The Essence of Maths Teaching for Mastery, published in June 2016, and in an earlier NCETM paper from autumn 2014.

Almost half of primary pupils miss new Sats standard

From the BBC:

Official data shows just over half (53%) of 11-year-olds made the grade in reading, writing and mathematics. […]

Department for Education statistics show:

  • 66% of pupils met the standard in reading
  • 70% in maths
  • 72% in grammar, punctuation and spelling
  • 74% in the teacher-assessed writing

The overall figure of 53% relates to the number of pupils who reached the expected standard in all three subjects.

Read the full story.

Richard Feynman on Teaching Math to Kids

A post on Farnam Street. A quote:

Feynman knew the difference between knowing the name of something and knowing something. And was often prone to telling the emperor they had no clothes as this illuminating example from James Gleick’s book Genius: The Life and Science of Richard Feynman shows.

Educating his children gave him pause as to how the elements of teaching should be employed. By the time his son Carl was four, Feynman was “actively lobbying against a first-grade science book proposed for California schools.”

It began with pictures of a mechanical wind-up dog, a real dog, and a motorcycle, and for each the same question: “What makes it move?” The proposed answer—“ Energy makes it move”— enraged him.

That was tautology, he argued—empty definition. Feynman, having made a career of understanding the deep abstractions of energy, said it would be better to begin a science course by taking apart a toy dog, revealing the cleverness of the gears and ratchets. To tell a first-grader that “energy makes it move” would be no more helpful, he said, than saying “God makes it move” or “moveability makes it move.”

Read the full story.

Mathematics in the news this week

France DGSE: Spy service sets school code-breaking challenge

France’s external intelligence service, the DGSE, has sponsored a school competition to find the nation’s most talented young code-breakers.

It is the first time the DGSE has got involved in such a project in schools.

The first round drew in 18,000 pupils, and just 38 competed in the final on Wednesday, won by a Parisian team.

 

STEM Competitions Motivate Students :

“The main message is mathematics is not about numbers and figures,” [Mark] Saul said. “It’s about figuring things out. Whenever you’re figuring something out, you’re doing something mathematical.”

Rebecca Hanson Launches A Breakthrough in Maths Teaching for Primary Students :

Rebecca Hanson has opened her agency Authentic Maths to help Primary School Teachers in the UK offering solutions to the difficulties being experienced with the implementation of the Government’s changes to the primary mathematics curriculum.

UK follows Russia’s example to set up specialist sixth form maths colleges:

A key figure in the establishment of specialist maths institutions in the UK was Baroness (Alison) Wolf, a professor at King’s College London. She knew about Russian maths skills because of her work in universities, where maths departments often attract a fair few Russian academics.

Initially, the idea in the UK was for universities to set up a nationwide network of specialist maths schools. However, only King’s College London and Exeter have taken the plunge.

Alexandre Borovik: Decoupling of Assessment

BBC reported today that

Thousands of parents in England plan to keep their children off school for a day next week in protest at tough new national tests, campaigners say.

Parents from the Let Our Kids Be Kids campaign said children as young as six were labelling themselves failures.

In a letter to Education Secretary Nicky Morgan, they said primary pupils were being asked to learn concepts that may be beyond their capability.

The government said the tests should not cause pupils stress.

These new tests, known as Sats, have been drawn up to assess children’s grasp of the recently introduced primary school national curriculum, which is widely considered to be harder than the previous one.

The letter from the campaign, which says it represents parents of six- and seven-year-olds across the country, says children are crying about going to school.

There is a simple solution – decoupling of assessment of schools from assessment of individual children.

As far I remember my school years back in Soviet Russia of 1960s, schools there were assessed by regular (but not frequent) “ministerial tests”. A school received, without warning, a test paper in a sealed envelope which could be open only immediately before the test; pupils’ test scripts were collected, put into an enclosed envelope, sealed and sent back. Tests were marked in the local education authority (and on some occasions even a step up in the administrative hierarchy — in the regional education authority); marked test scripts, however, were not returned to schools, and schools received only summary feedback — but no information about performance of individual students.

This policy of anonymised summary tests created a psychological environment of trust between pupils and the teacher — children knew that it was not them who were assessed, but their teacher and their school, and they tried hard to help their teacher. Good teachers could build on this trust a supportive working environment in a classroom.  Schools and teachers who performed well in such anonymised testing could be trusted to assess pupils in a formative, non-intrusive, non-intimidating way — and without individual high stakes testing.

Of course, all that are my memories from another historic epoch and from the country that no longer exists. I could be mistaken in details, but I am quite confident about the essence. In this country and in recent years, I happened to take part in a few meetings in the Department for Education, where I raised this issue. Education experts present at these meetings liked the idea but it was not followed by any discussion since it was outside of meetings’ agenda — we had to focus on the  content of the new curriculum, not assessment. I would love to see a proper public discussion of feasibility of decoupling.

I teach mathematics at a university. I think I am not alone (I heard similar concerns from my colleagues from Universities from all over the country) in feeling that many our students come to university with a deformed attitude to assessment — for example, with subconscious desire to forget everything as soon as they have sat an exam. It could happen that some of them, in their school years, suffered from overexamination but were not receiving  sufficient formative feedback. At university, such students do not know how to use teachers’ feedback. They do not know how to ask questions. Could it happen that the roots of the problem could be traced back to junior school?

Disclaimer. The views expressed do not necessarily represent the position of my employer or any other person, organisation, or institution.

Alexandre Borovik