http://www.bbc.co.uk/news/education-29599177 ]]>

I do not like the way statistics is explained in the MEI‘s draft “Critical Maths” Curriculum.

It appears from “Mathematical ideas which students should encounter through discussion of problems” (p. 8 of the document) that students are supposed to learn, understand, and apply the three basic limit theorems of probability theory/theoretical statistics:

* the (strong) law of large numbers — “average in time converges to average in space”;

* the central limit theorem — “all roads lead to Rome” (where “Rome” is the standard normal distribution);

* empirical distribution converges to theoretical distribution (Glivenko-Cantelli theorem).

I would prefer these three goals being presented in a more definite way, and then reformulated in practical terms, with a number of applications. At the moment, there is no any structure here.

A few more comments.

Page 9: Graph of a normal distribution is wrong: it must be strictly

positive everywhere!

“Very unlikely” does not mean “never happens”.

By the way, why there is 2\sqrt{n}, and not 3\sqrt{n}?

]]>*Children who enter school at six or seven – after several years of high quality nursery education – consistently achieve better educational results as well as higher levels of wellbeing. The success of Scandinavian systems suggests that many intractable problems in English education – such as the widening gap in achievement between rich and poor, problems with boys’ literacy, and the ‘summerborns’ issue – could be addressed by fundamentally re-thinking our early years policies.*

It’s a learned behavior because at some point of your life , not even knowing ‘when’ you decided you’re not good at mathematics. And so, your math phobia was born.

Many people develop a phobia about math because of certain events in their past…

…it could be any teacher who have criticized you or embarrassed you in front of the class when you made some mistakes solving a math problem…

…it could be your lack of understanding of some basic concepts of mathematics which you never caught up with everyone else…

…It could be your parents also who would have scolded you and discouraged you and have put a question mark on your ability to take up mathematics for further studies…

GENDER DIFFERENCE

Another important reason behind Mathematics phobia is believed to be gender difference. A general trend is often seen that girls are more phobic to Mathematics than boys. Girls are basically anxious in nature .Besides most of our elementary school teachers are women and it is seen that they often pass their anxiety or phobia towards the subject to their students and gradually a girl also starts believing that she cannot excel in the subject . From a research conducted on 566 male and 567 female students aged between 11 – 13 years in both single sex and co-educational school it has been found that Humanities and English are mostly preferred by girls while boys are more inclined towards Physical Education , Science and Mathematics .

TEACHER’S BEHAVIOUR

Teachers behavior overtly or covertly influences the classroom atmosphere by affecting their emotional responses, beliefs and behavior related towards Mathematics . Teachers serves as mentor and they are role model to their students .They should be careful enough about how their attitude towards Mathematics can affect a student. Teachers who belief about utility of Mathematics are often found to correlate with either a more positive or negative attitude towards the subject .If a teacher believes Mathematics have little utility in our daily life she will have a negative attitude towards the subject . And this negative attitude will be inculcated to their students. Teachers have to enhance their understanding the subject . Only sound knowledge in the subject will not be enough for a teacher to motivate his or her students. A teacher has to remember, Mathematics anxiety does not come from the subject itself but from the way the subject is presented in the school.

So you get the best of both worlds!

]]>“Here is a fraction with big numbers that you have never seen before: 36/54. Do you think it could be equal to a simpler fraction which you have come across before? Which one?”

The food is now in the child’s stomach, which contains, however, no knowledge of the 6 times table. How will the child digest this food?

This is you a very good problem for a [suitable] child because it is Richly Complex rather than Falsely Simple.

]]>David Tall (27 May 2012) implicitly queried this claim, and I agree with him. It would be better to say, “The act of devising a curriculum is inevitably a top-down process AND a bottom-up process, as drafters select and interpret certain higher objectives and experts in children’s mathematical development relate them to children’s capacities at different ages.”

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