Brain works in sleep

Many mathematicians believe that that their brains continue to do mathematics during sleep. A paper

Kouider et al., Inducing Task-Relevant Responses to Speech in the Sleeping Brain, Current Biology (2014), http://dx.doi.org/10.1016/j.cub.2014.08.016

Proves that brain continues in sleep some mental activities of the day.

From the summary of the paper:

using semantic categorization and lexical decision tasks, we studied task-relevant responses triggered by spoken stimuli in the sleeping brain. Awake participants classified words as either animals or objects (experiment 1) or as either words or pseudowords (experiment 2) by pressing a button with their right or left hand, while transitioning toward sleep. The lateralized readiness potential (LRP), an electrophysiological index of response preparation, revealed that task-specific preparatory responses are preserved during sleep. These findings demonstrate that despite the absence of awareness and behavioral responsiveness, sleepers can still extract task relevant information from external stimuli and covertly prepare for appropriate motor responses.

The paper generated a huge response in mass media: BBC, New Scientist, NBC News. It is mentioned in this blog because the study of brain activity  is relevant to mathematics education. A naive question: do our students get enough sleep?

Citizen Maths MOOC

An experimental MOOC (Massive Open Online Course) Citizen Maths is launched and the first phase of the course is open for registration. It is free and open for everyone; its motto is Powerful Ideas in Action.

The readers of this blog may like to register for the course, because, as the organisers say,

The success of this first phase of Citizen Maths will depend crucially on the feedback that we obtain. We are particularly keen to get feedback from:

  • learners who do the course;
  • those with an interest in the learning and teaching of maths, and in the design of online courses.

There is a link to a feedback form on every page of the Citizen Maths web site, and there will be a similar link on every page of the course when it goes live on or around 12 September.

The first pilot stage will run for four weeks and cover the first “powerful idea”: proportion. An admirable choice (a detailed discussion of the role of proportions in elementary mathematics can be found in this paper by Tony Gardiner).

Maryam Mirzakhani, the first woman to win Fields Medal

Maryam Mirzakhani

From Maryam Mirzakhani’s interview to the Clay Institute:

My older brother was the person who got me interested in science in general. He used to tell me what he learned in school. My first memory of mathematics is probably the time that he told me about the problem of adding numbers from 1 to 100. I think he had read in a popular science journal how Gauss solved this problem. The solution was quite fascinating for me. That was the first time I enjoyed a beautiful solution, though I couldn’t find it myself. [...]

I was very lucky in many ways. The war ended when I finished elementary school; I couldn’t have had the great opportunities that I had if I had been born 10 years earlier. I went to a great high school in Tehran – Farzanegan – and had very good teachers.[...]

Our school was close to a street full of bookstores in Tehran. I remember how walking along this crowded street, and going to the bookstores, was so exciting for us. We couldn’t skim through the books like people usually do here in a bookstore, so we would end up buying a lot of random books. Also, our school principal was a strong-willed woman who was willing to go a long way to provide us with the same opportunities as the boys’ school.

Later, I got involved in Math Olympiads that made me think about harder problems. As a teenager, I enjoyed the challenge. But most importantly, I met many inspiring mathematicians and friends at Sharif University. The more I spent time on mathematics, the more excited I became.

Read the full text of the interview at The Guardian website.

Programmes of study for Mathematics at Key Stage 4

Programmes of study for  Mathematics at Key Stage 4, which will be taught in schools from September 2015 alongside the new English and mathematics GCSEs, are published today. This appears to be the final pack of statutory documents:

Can you pass the maths test for 11-year-olds?

A sample KS2 test based on the official publication from Standards and Testing Agency,
2016 key stage 2 mathematics test: sample questions, mark scheme and commentary,
was published in The Telegraph. One question attracts attention. In The Telegraph version, it is

A question as published in The Telegraph.

The answer given is £12,396.

And this is the original question from 2016 key stage 2 mathematics test: sample questions, mark scheme and commentary

The official version of the same question

In my opinion, both versions contain serious didactic errors. Would the readers agree with me?

And here are official marking guidelines:

Official marking guidelines

And the official commentary:

In year 6 pupils are expected to interpret and solve problems using pie charts. In this question pupils can use a number of strategies including using angle facts or using fractions to complete the proportional reasoning required.
Pupils are expected to use known facts and procedures to solve this more complex problem. There are a small number of numeric steps but there is a demand associated with interpretation of data (or using spatial knowledge). The response strategy requires pupils to organise their method.

Mathematics after 16: the state of play, challenges and ways ahead

On Wednesday 02 July the Nuffield Foundation published report Mathematics after 16: the state of play, challenges and ways ahead. It argues that reforms to GCSEs and A levels risk undermining the government’s goal of universal participation in post-16 mathematics education, particularly if new ‘Core Maths’ qualifications are not backed by universities. The report brings together a wide range of evidence and warns that plans to make GCSE Maths more demanding, detach AS from A levels, and replace the modular structure in favour of terminal exams could actually discourage students from continuing to study the subject beyond the age of 16.

The report is available to download from the Nuffield Foundation website.