Integral – the
future
Aims of this session
• To take stock of the current Integral and to tell
you about how it is being developed
• To allow you to get ‘hands-on’ with upcoming
new resources for Integral
• To discuss what you would like to see from
maths resources in the future, particularly in the
light of forthcoming changes to Mathematics and
Further Mathematics A levels
Which needs does Integral seek to meet?
We hope resources in Integral meet the needs of
a) Teachers who are new to a topic and looking to
get a firm grounding as well as ideas.
b) Teachers who are experienced with a topic and
looking for new ideas.
c) Teachers looking for guidance with planning and
resources for homework/classwork.
d) Students working at a range of ability levels.
e) Students working in class or studying
independently.
How does Integral support teachers?
• Provides teachers with a solid knowledge
foundation through notes, crucial points and worked
solutions, interactive resources
• Integral seeks to support teachers’ own interaction
with students through classroom activities and
discussion ideas.
• Provides teachers with plenty of exercises and
tests.
• The topic/section structure in Integral can inform
schemes of work.
Teaching Resources
• Don’t miss these - there are many gems:
•
Ask students to list pairs of functions f(x) and g(x) such that fg(x)=x. These can range from very
simple ones such as f(x)=x+2 with g(x)=x−2 through
to f(x)=ex and g(x)=ln(x) or f(x)=√x and g(x)=x2.
Explain that g(x) and f(x) are said to be the inverses of each other. Introduce the notation of f−1(x).
Investigate the link between the graphs of f(x) and f−1(x). shown in this example:
• Interactive Resources:
Survey of Integral users – teachers’
use of Integral
The way that Integral supports classroom teaching
came through very strongly in the survey:
❖popularity of active learning resources
❖popularity of teaching resources
❖requests for more of these where they are more
sparse
❖requests for more ideas about how to introduce
topics
How does Integral support students?
• The origins of Integral are as a resource to
support a student’s independent self-study (of
Further Mathematics) so it still provides much
guidance of this kind – particularly study plans.
• It provides opportunities for informal practice of
basic techniques.
• Section tests allow self-monitoring of progress.
Anecdotally at least they are a very good
indicator for success in examinations.
Survey of Integral users - students’ use
of Integral
• Some teachers use Integral to facilitate
independent learning by students, some are
experimenting with ‘flipped learning’
• This is particularly true for Further Mathematics
• Most teachers said that they would like a
resource which would encourage even more
independent learning (whilst freely admitting that
this is a work in progress in many cases!)
Development of new Integral content
• We are conducting a review of C1 - C4, FP1, FP2,
M1-M2, S1-S2 resources by teachers who have
experience of using them to seek ideas to extend
active learning and teaching resources
• Three levels of written exercise for each section
Level 1 – basic skills;
Level 2 – working to examination standard;
Level 3 – extension questions.
Problem-solving questions will appear
throughout.
Development of new Integral content
Development of learning ‘Walkthroughs’
to cover all of A level Mathematics and
Further Mathematics:
a walkthrough is a sequence of activities, most of
which are based on Geogebra, which students can
follow independently or in class to explore the initial
ideas in an area of mathematics.
Development of new Integral content
Development of ‘Skill Packs’ to cover all
of A level Mathematics and Further
Mathematics
a skill pack is a series of examples and
questions where students can learn and practise
the basic skills, techniques and formulae
required for a section of learning.
Development of new Integral content
• ‘Active Learning with Geogebra’ worksheets
Development of new Integral content
• ‘Videos of students working with teachers on
problem-solving tasks
• We have considered the possibility of other
video resources (skills videos, worked solutions)
Other Integral development
Reviewing and developing the look and feel of the
site. This will include:
• site navigation
• performance on mobile devices
• the layout of the section page to emphasise a
route through the learning
• organising the teaching resources so as to make
them more prominent
Integral for new AS/A levels
Headline changes:
• All A levels now linear.
• AS can be co-taught with A level, but will have a
separate exam which will not count towards the
A level.
• The intention is that AS can be taught as the
first half of A level though it need not be.
• AS content will be examined at A level standard
in the A level examination but at AS standard
for the AS qualification.
• AS can be taught over 1 year or 2 years.
Integral for new AS/A levels
Content
• Problem-solving
• Compulsory mechanics in A level Mathematics
• Compulsory statistics in A level Mathematics
including
use of large data sets (these may be
provided by exam boards) and use of
technology to explore and interpret them
• Further Mathematics to retain optional content
For discussion
• What might be the best way to divide up the
content in Integral for new linear A levels?
• What sort of materials would you value to help
with the problem-solving aspect of the new
courses?
• What sort of materials would you value to help
with working with the large data set?
For discussion
• Do you want more resources to support
students’ independent learning?
• Are there any particular resources that are
needed for Further Maths (particularly given
ever increasing pressures on the funding of
Further Mathematics)?
For discussion
• Would you like to see any changes to the look,
navigation or general functionality of the site?
• How important is it that the site works well on
tablets?
For discussion
• Are the links to between Integral and textbooks
important to you?
• Would you like to see Integral expanded to
include GCSE mathematics? Or parts of GCSE
mathematics?
About MEI
• Registered charity committed to improving
mathematics education
• Independent UK curriculum development body
• We offer continuing professional development
courses, provide specialist tuition for students
and work with industry to enhance mathematical
skills in the workplace
• We also pioneer the development of innovative
teaching and learning resources