Mathematics Matters
#MathsMatters
Richard Gould
rg@villierspark.org.uk
Innovative approaches to address
underachievement amongst
disadvantaged secondary school
age students with high academic
potential
Evidence of underachievement
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Worldwide research suggests that about 25% of the most able (‘Gifted &
Talented’) achieve below their peer group average
Professor Margrit Stamm (Switzerland); Professor Françoys Gagne (Canada)
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One UK researcher compared performance between the end of primary and
the end of secondary school in an attempt to measure underachievement.
Only one third of the children aged 11 in 1999 who ranked in the top 5%
using scores in Key Stage 2 Maths and English achieved three A grades in
A-level examinations at age 18
“This means that, of the 30,000 children classified as Gifted and Talented using raw
scores for KS2…less than a third are realising their potential seven years later. This
is a tragic waste of natural talent.”
Professor David Jesson, University of York (UK)
Why the underachievement?
Lack of challenge in the classroom
Learning style different to classroom norm
Don’t want to stand out
Poor motivation
Entrepreneurial giftedness
Evidence of the gap for disadvantaged able students
There is a 17 percentage point attainment gap at age 11 between Free
School Meal pupils (FSM) and others, measured by the attainment of Level
4 in Mathematics and English. The gap rises to 22 percentage points for Alevel attainment at age 18
Department for Education data for 2012
“The odds of a child at a state secondary school who is eligible for free
school meals in Year 11 gaining a place at Oxford or Cambridge by the age
of 19 is almost 2,000 to 1 against. By contrast, the odds of a privately
educated child being admitted to Oxbridge are 20 to 1.”
Social Mobility & Child Poverty Commission, June 2013
Why the gap?
Low self-esteem
Inadequate study skills
Poor motivation
Low aspirations
Insufficient peer and family role models
At schools with poor attainment so hard to recruit and retain the best teachers
No recognition of the impact of education on life chances
Culture – lack of awareness of ‘the game’
Inspiring Excellence Programme
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210 online extension activities including Mathematics –
challenging able post-16 students to tackle topics
beyond their examination specification
Subject-specific residential courses for able post-16
students including Mathematicians – introducing the
latest developments and research; developing the skills
needed to bring expertise
Advisory Service support to schools and colleges to
raise the level of challenge in the everyday secondary
school classroom
Inspiring Excellence Programme
Online extension activities in Mathematics
– free resources at www.villierspark.org.uk
Each one features:
• An introduction film
• The activity
• Suggested response provided by
activity writer
Activity 1: The Koch Snowflake and Fractal Friends
http://www.youtube.com/watch?v=yy7uy_63Rk4
The Koch Snowflake & Fractal Friends
Target Audience: Mathematics students interested in extending their understanding of geometry and keen
to explore theoretical and practical examples of fractals.
Key Concepts: Lengthscales, self-similarity, generalised dimension, geometric progressions.
The Activity: The snowflake is formed by beginning with the “Star of David”, a regular 12-sided polygon
composed of 12 equilateral triangles. It is modified by adding more triangles in the centre of each side, each
side of 1/3 the previous length. How does this change the original area and perimeter? If we repeat the
process indefinitely, what do the final area and perimeter tend to? What percentage of the circle surrounding
the original star is this area? Investigate the concept of fractional dimension to evaluate the dimensionality of
this and other fractal objects.
Background Knowledge: Basic trigonometry, sum to infinity of geometric progressions, logarithms.
Resources: There is a wonderfully varied introduction to the subject in general at the Fractals Unleashed
website. Websites abound for those of an artistic bent, one such striking example here providing light relief.
Outcomes: This is an obviously visual subject, so why not give a presentation on your findings? Even
better, incorporating an animation of fractal processes is a great way to illustrate their properties.
Helpful hints: How does the number of smaller triangles added to the snowflake at each iteration change?
What about the area of these triangles? Can you relate this to a sum to infinity for the area? Use the
coastline measurement problem to get a feel for self-similarity and fractional dimension. How does our
measurement of perimeter/area/volume for these shapes depend on the length of our ruler?
Some diagrams from the suggested response: The Koch Snowflake & Fractal
Friends