# Children to be marked up for using long division in maths

Long division and multiplication will make a return to maths exams as part of a Government drive to boost standards in primary schools, it will be announced today.

Pupils aged 11 will be given extra marks for employing traditional methods of calculation in end-of-year Sats tests, it emerged.

Children who get the wrong answer but attempt sums using long and short multiplication or adding and subtracting in columns will be rewarded with additional points.

Ministers insisted the changes – being introduced from 2016 – were intended to stop pupils using “clumsy, confusing and time-consuming” methods of working out. […]

Elizabeth Truss, the Education Minister, will outline the plans in a speech to the North of England Education Conference in Sheffield on Thursday.

Speaking before the address, she said: “Chunking and gridding are tortured techniques but they have become the norm in recent years. Children just end up repeatedly adding or subtracting numbers, and batches of numbers.

“They may give the right answer but they are not quick, efficient methods, nor are they methods children can build on, and apply to more complicated problems.

“Column methods of addition and subtraction, short and long multiplication and division are far simpler, far quicker, far more effective and allow children to understand properly the calculation and therefore move on to more advanced problems.”

# Calculators banned in primary school maths exams

Calculators are to be banned in primary school maths exams as part of a Government drive to boost standards of mental arithmetic, it was announced today.

Pupils will be required to complete sums using pen and paper amid fears under-11s in England are already more reliant on electronic devices than peers in most other countries.
The change – being introduced from 2014 – coincides with the publication of a draft primary school curriculum that recommends delaying the use of calculators as part of maths lessons.
Currently, children are expected to use them at the age of seven, but this is likely to be put back to nine or 10 under the Coalition’s reforms.
Elizabeth Truss, the Education Minister, said that an over-reliance on calculators meant pupils were failed to get the

rigorous grounding in mental and written arithmetic that they needed to progress onto secondary education.
Pupils should not use the devices until they know their times tables off by heart and understand the methods used to add, subtract, multiply and divide, she said.

# Rethinking maths for the 21st century

From Research News on the University of  Cambridge website:

An exciting new Maths Education Programme is being launched by the University of Cambridge which aims to provide innovative, rich and stimulating materials to help support and inspire teachers and students of advanced post-16 mathematics.

The Project will receive £2.8 million from the Department for Education over the initial three years of the five year project, with a review after three years.

It will be led by Professor Martin Hyland, head of the Department of Pure Mathematics and Mathematical Statistics, and Lynne McClure, director of NRICH, part of

the University’s Millennium Mathematics Project.

The programme will seek to reconsider and rethink how changes in our understanding of maths impact on the mathematics which is studied at school level. The past few decades have seen advances in our understanding of core mathematics, major developments in areas such as probability and the emergence of new disciplines, including mathematical biology.

It will provide rich resources for advanced post-16 mathematics which will augment and support current teaching, be published online and be freely accessible to all. The emphasis will be on simple underlying mathematical ideas, helping students to explore connections between different areas of mathematics, and supporting the development of key mathematical skills and clarity of thought. The impetus for the programme comes from a belief in the importance of dialogue between schools, higher education and research.

Building on the University of Cambridge’s long history of working with schools, for instance through the Millennium Mathematics Project, researchers will consult widely with teachers during the development of the programme. While individual students will also be able to work through the resources independently, the project will provide extensive teacher support material to encourage classroom use. In addition, the programme will include professional development summer schools for teachers. The University of Cambridge programme will also work closely with other organisations supporting advanced post-16 mathematics.

It is anticipated that pilot versions of material will begin to be published next summer, with development continuing over the following two years.

Professor Hyland says: “We are very grateful for this opportunity to share thinking about the major themes in mathematics with teachers. One of the key aims of the project is to provide material to support inspirational and committed teachers in exploring the subject beyond curriculum boundaries, leading to a richer educational experience for all.”

# Cambridge University 'to set maths A-levels'

From  ‘s article in The Telegraph:

Leading mathematicians are to script new syllabuses and exam questions as part of radical reforms being introduced to drive up education standards.

Revised qualifications will feature an emphasis on key disciplines such as trigonometry and probability, “demanding” questions will be set to stretch the brightest pupils and lesson materials will be available online.

The move is designed to address major concerns over a sharp decline in teenagers’ maths skills – leaving hundreds of thousands of young people unfit for the demands of higher education.

Cambridge warned that even the most talented students did not have “sufficient mastery of basic mathematics” and existing A-levels were too “superficial”.

Academics including Sir Tim Gowers, who won the prestigious Fields Medal for mathematics in 1998, will be involved in the project, although it could lead to a significant delay in the introduction of new sixth-form exams. […]

A source close to Michael Gove said: “It is vital we raise standards, raise ambition and get people who really understand subjects back in charge.

“It is incredibly exciting that some of the best mathematicians in the world want to fix A-level maths. This will spread understanding of teaching the deep problem-solving skills that are so vital to universities and businesses, and give many more pupils an advanced education.”

Cambridge’s Department of Pure Mathematics has submitted a report to the Department for Education outlining how new-style maths A-levels should be structured.

It claims that changes are needed because “the majority of the talented students which Cambridge is able to recruit do not have sufficient mastery of basic mathematics to enable them to confidently engage with anything other than routine problems”.

“Existing A-level curriculums treat topics superficially and the UK has lost the tradition of teaching school mathematics coherently and in depth,” it adds. “The effect on Cambridge is acute.”

The document, by Prof Martin Hyland, head of the department, suggests focusing A-levels around a series of “key mathematical ideas”. This is likely to include complex numbers, trigonometry, combinatorics, probability and centres of mass.

In a key change, it recommends creating “graded sets of problems” for bright teenagers. A major part of assessments will be addressed at all students, but Cambridge is proposing a “range of demanding questions to challenge the most able”.

Academics are pledging to “exploit the potential of the web” by making maths materials available online and creating a newly-constructed website for teachers’ feedback.

Mathematicians from other universities will be asked for their input into the new A-level, which will extensively trialled in schools.

But the move is likely to lead to an overall delay

to the introduction of new-style qualifications in the subject, with Cambridge suggesting they could take five years to develop.

The Department for Education originally suggested it wanted new A-levels to be taught for the first time in 2014, although the Cambridge plan would rule out major changes until 2017 at the earliest.

# A view from USA: "Why can't we teach math?"

From a post  The School CEO: Why can’t we teach math? by  Jeanne Whitmore in American Fork Citizen, 29 September 2012:

I had a parent ask me why we don’t teach Compass and Straight edge Geometry anymore. Thank goodness he gave me a link to the Wikipedia article to explain what it is. (Here it is if you are interested.) I would love to explain to him why we don’t teach this particular type of geometry, but I don’t know. I couldn’t teach it; I don’t know if I could learn it.

But why could we teach it at one point, and we can’t now? As a Charter School CEO, it is difficult to get math and science teachers. Math and science teachers can make a lot of money in the private sector and schools have difficulty competing.

Mathematicians can earn a median wage of $99,000 and people in Math and Science occupations earn a median income of$74,040. It’s no surprise that people with Math backgrounds don’t want to earn a starting salary of less than $30,000 per year at an elementary school or high school. Granted there are teachers who only desire to teach and love the atmosphere of the school, but these are few and far between. A school would be lucky to get a great mathematician who has already retired from a non-education career then decided to teach as a second career. But, let’s assume that mathematicians have always earned a much higher income than the general population. Why was it possible to hire a mathematician in the 40’s and 50’s, but not now? Well, the jobs that can use mathematics have exploded. Whole classes of occupations didn’t exist in the 40’s that exist now. Look at this list of occupations: Actuary, Computer programmers, Computer Systems Analyst, Database Administrators, Financial Analyst, Market Research Analyst, Nuclear Engineer, Operations Research Analyst, Statistician and Survey Researcher. Many of these classes of jobs didn’t exist in the 40’s and even if they did exist, the computer revolution and Internet have enabled massive data collection that have increased the number of jobs in every field related to data analysis and statistics. A research paper published in the National Bureau of Economic Research in 1957 showed that 87.4% of mathematicians worked in colleges and universities. Now, only 16% work in education with 63% working in the Federal Government and Scientific Research. We can’t compete with the increasing demand for mathematicians from the private sector in salaries, benefits or work environment. But, if we can’t teach math in elementary and high school to the same standards we did in the 40’s and 50’s where will our next generation of mathematicians come from? It is almost like the worm eating its own tail. We are chewing up the mathematicians we created in previous generations and we are not creating the new generations of mathematicians to take their place. Today we can’t have a math teacher teach “Compass and Straight edge Geometry” because they were not taught that by their teachers. Jeanne Whitmore is the founder and CEO of American Fork charter school Aristotle Academy, and an education columnist for the American Fork Citizen. Here is the document cited in the post: Study of math profession occupations, 1957. # Is algebra necessary, Part II A lively discussion of Andrew Hacker’s op-ed Is Algebra Necessary? in the New York Times (see previous post) continues. Evelyn Lamb ‘s op-ed on the Scientific American website, Abandoning Algebra Is Not the Answer, a quote: What is algebra anyway? It’s a huge subject, but at its heart, it’s about relationships. How does a change in one quantity affect another quantity when they are related in a certain way? Hacker suggests that we need arithmetic but don’t need algebra. But it’s really difficult to separate these two skills. Algebra and geometry, another subject Hacker could do without, help develop logical skills and abstract reasoning so we can understand why we are making less money than before if we get a 20 percent pay cut followed by a 20 percent raise (or a 20 percent raise followed by a 20 percent pay cut—hello, commutative law of multiplication!) or how much merchandise we can purchase if we have$100 and a 25 percent off coupon.

in Huffington PostAlgebra Is Essential in a 21st Century Economy. A quote:

One fallacy in Hacker’s reasoning is clear: Why single out mathematics? Yes, a knowledge of calculus may or may not help one negotiate through traffic or connect one’s computer to the Internet, but the same could be said for many other disciplines. How does knowing whom Hamlet killed accidentally help one be a better consumer? Does knowing the history of the Spanish-American War help one complete one’s tax return?

And see blogs by Rob Knop and RiShawn Biddle.

# Is algebra necessary? Yes, algebra is necessary

Two competing claims in the mainstream newspapers:

Andrew Hacker in The New York TimesIs algebra necessary? A brief quote:

There are many defenses of algebra and the virtue of learning it. Most of them sound reasonable on first hearing; many of them I once accepted. But the more I examine them, the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic.

Daniel Willingham in the Washington Post: Yes, algeba is necessary. A brief quote:

Hacker overlooks the possibility that the mathematics learned in school, even if seldom applied directly, makes students better able to learn new quantitative skills. The on-the-job training in mathematics that Hacker envisions will go a whole lot better with an employee who gained a solid footing in math in school. […]

[In]  teaching the specific skills that people need, you had better be confident that you’re going to cover all those skills. Because if you teach students the significance of the Consumer Price Index they are not going to know how to teach themselves the significance of projected inflation rates on their investment in CDs. Their practical knowledge will be specific to what you teach them, and won’t transfer.

The best bet for knowledge that can apply to new situations is an abstract understanding — seeing that apparently different problems have a similar underlying structure. And the best bet for students to gain this abstract understanding is to teach it explicitly.