Maths essentials


How practitioners can improve their maths online


By Danielle Watts I have recently taken on a new role as head of maths and English and my focus is on initiatives to improve the learning experience in these subjects across the college, both for students and staff. I quickly realised that many of


our vocational tutors have a real fear of maths. I set out to find approaches that would help the staff upskill their own strengths in the subject. I came across Citizen Maths,


a free, open online course for self-motivated adults who want to improve their grasp of maths. It gave our college the


opportunity to become part of the Citizen Maths Professional Development Exchange. This is a collaboration between Citizen Maths and the Education and Training Foundation. I was excited to have the chance to work with other Citizen Maths partners looking at professional development for FE staff who are not necessarily confident in teaching maths. So how will this help me? We’ve found that Citizen Maths enables staff to learn at their own pace, without having to sit in a lesson being taught


Finite Ideas


aed ae talian physicist Enrico Fermi who used estimation to help crack complex problems in physics and maths.


tudents oen beliee tat od obles ae one secific anse and one a of getting there. Fermi questions, on the other hand, encourage learners to estimate, eason, ake assutions e benefit is tat ei uestions can elate ats to the real world, and to vocational learning. A typical Fermi question is a very open question with little or no data provided. For example: • How many bags pass through Heathrow airport each day? • How many bottles of shampoo would a hair salon use in a year? • If you’re on a water meter, is it worth calling a plumber to mend a leaking tap? ei uestions ae used a lot in te ne eel  oe ats ualifications, but te


dieentiate ell and ae suitable o an leel, including unctional kills Have a look for useful examples of Fermi questions at goo.glSD7vp Or try searching for Fermi maths on the Internet.


INTUITION ISSUE 27 • SPRING 2017 23


by one of their colleagues. The online learning modules are a convenient and discreet way for them to do this, allowing them to upskill as part of their own professional development. It has given them more confidence in approaching mathematical ideas when maths is embedded into their teaching. We are now in the process of sharing access with all staff and using Citizen Maths for targeted continuous professional development. We believe if we have confident staff, we will foster confident learners.


o find out oe about Citizen Maths go to


goo.gl/YYKKNn See a video of


Danielle talking about Citizen Maths at goo.gl0GAe


FRACTIONS One hurdle that causes many learners to stumble and fall is fractions. An excellent free resource, with lots of practical ideas on teaching, is the Fractions booklet from the National Research and Development Centre for adult literacy and numeracy (NRDC). The booklet is available at goo.gl/4Ksh3Q


Danielle Watts is head of maths and English (16-18) at Barking & Dagenham College


MULTIPLE REPRESENTATIONS Fractions lend themselves to visual images, and learners’ understanding of fractions will be enanced b oking it dieent representations – for example area diagrams, number lines, words, symbols, and decimal and percentage equivalents. Fractions should also be related to objects that learners frequently come across in their vocational learning and daily life (e.g. a chocolate bar, tape measure or clock face). For good examples see pages 14


and 15 in the NRDC booklet or visit STEM Learning at goo.glDt5O


MISCONCEPTIONS There are several common errors and misconceptions related to fractions, oen inoling oegenealisations from learning with whole numbers. For example, learners may


consider 1/8 to be larger than 1/5 (as 8 is larger than 5), and 1/4 + 1/3 = 2/7 is not uncommon. A useful activity is asking learners


to discuss and ealuate dieent statements about fractions. For example: • A fraction is a small piece of a whole;


 ie is less tan si, so onefi ust be salle tan onesit


• Any fraction can be written in lots o dieent as


Steve Padoe is a maths specialist ITT tutor and the ETF’s regional maths coordinator in the West Midlands.


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