InnovateInnovateIssue 4, July 2013Issue 4, July 2013

www.oakgrove.milton-keynes.sch.ukwww.oakgrove.milton-keynes.sch.uk

the teaching and learning magazine for Oakgrove School

NumeracyNumeracyacross the curriculumacross the curriculum

In the Spotlight

In the spotlight

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Developing literate and numerate students is something that we, as teachers, are all responsible for. It is important to all of us that students leave school with a solid understanding of words and numbers, in order for them to go on to be self-suffi cient in the future.

One of the biggest problems that we encounter in the Maths De-partment is a fear of numbers that has been passed on to students from the adults around them. Th rowaway comments from home or the media can combine to turn a maths problem into some-thing insurmountable. Celebrities will oft en claim to be ‘rubbish at maths’, whereas being ‘rubbish at reading’ is not seen as equally acceptable. Parents evenings are oft en fi lled with comments such as: ‘no-one in the family has ever been good at maths so it’s no surprise that Bob isn’t either’ and ‘I was never any good at maths but it hasn’t done me any harm’.

Integrating numeracy into lessons and allowing students to see its applications across the curriculum will go some way towards tackling this. Th e ideas and resources in this issue of Innovate are designed to act as prompts for your planning. Estimating, graph-ing, problem solving, interpreting and analysing are all part of the numerate students toolbox. Most important, is developing a culture of mathema cal confi dence, in both staff and students. If maths is discussed in a posi ve way inside school, we hope it will start to counter the nega ve messages students pick up on outside of school.

Defi nition of numerate: adjective having a good basic knowledge of arithmatic; able to under-stand and work with numbers

By Emma Cox

As part of the TELL group’s work on Numeracy, Sally Newton joined with our work experience student, Meera Chudasama, to gather Yr 10 student views and perceptions of Numeracy across the curriculum. Th is resulted in a very interesting article and a fantastic Numeracy mindmap, created by Meera.

Finally, at the end of the magazine, we explore some practical ideas for Inquiry based learning from the Drama, History and Psychology departments.

As always, I am very grateful to all those who have contributed to this edition: Ben Robinson, Annie Handyside, Jennie Long, Meera Chudasama, Sally Newton, Jo Johnston, Niamh Bland, Jo Green, Alan Nicholl, Martin Squires and Emma Cox.

Enjoy reading!

Charlotte Hawker.

Welcome to the fourth edition of our teaching and learning magazine. Th is is an edition of ‘fi rsts’ for many reasons: we have the widest range of subject contributions from across the school, we have an article based entirely on student views and we apply Mathematical principles to inquiry based learning.

As our second edition of the magazine focused on Lit-eracy across the curriculum, the TELL group thought that an edition based on Numeracy was well over-due! Emma Cox, who instigated the idea, has introduced the premise of this edition in ‘In the Spotlight’ below.

We start with an entertaining and enlightening article from Alan Nicholl, where he deconstructs the ste-reotypical view that Mathematics and the Arts are at opposite ends of the academic spectrum.

Next, we move onto our ‘Numeracy in the classroom’ section, where we feature contributions from PE, Ge-ography, History and MFL.

Contents

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pg 12-13 cont. on pg 14 -15

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pg 6-7

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pg 14-15

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Th e elegance of numbersBy Alan Nicholl

Numeracy in the classroomBy Ben Robinson in PEBy Martin Squires in Geography

Could you be a Roman Trader? By the History Department

Numeracy in the MFL classroomBy Jo Johnston, Jo Green and Niamh Bland

How students view NumeracyBy Sally Newton and Meera Chudasama

Using Mathematical Principles for inquiry based learningBy Annie Handyside and Jennie Long

The Elegance of NumbersBy Alan Nicholl

Obviously, we all know that Maths and the Arts, including Literature, don’t mix. Maths is about numbers, patterns and logic; Literature is about

words, randomness and feelings. However, consider this quotation: “Pure mathematics is, in its way, the poetry of logical ideas.” Or this: “Poetry is the best words in their best order.” Or this: “A mathematician, like a painter or poet, is a maker of patterns.” These are not the words of Mr Barnes, though I’m sure he has thought these things on numerous occasions, but were written by Albert Einstein, Samuel Taylor Coleridge and GH Hardy (disappointingly for the purposes of this article, no relation to Thomas), respectively. When we further consider the fact that Miss Hawker disproved Fermat’s little theorem, which states that if p is a prime number, then for any integer a, the number a p − a is an integer multiple of p, whilst still at Earls Barton primary school and the surprising dis-covery that Mr. Boyce has written over one hundred Petrarchan sonnets proclaiming his love of all things mathematical (see below), the idea of a supposed divide between Mathematics and Literature becomes harder to sustain.

Ode To Euclid

Thy Elements written in ancient Greek, Thy sweetest axioms beyond compare, Method of exhaustion oh so rare. To my broken heart thy theorems speak. Oh Euclid, Euclid with thy thoughts sublime, Avidly read when I was but a boy, Thy parallel postulate sings with joy. Thou art not for an age but for all time. And yet at Oakgrove canst thou still be heard? Or are we deaf to your propositions? Drowned by electronic calculations, With our philistine minds no longer stirred. Still I yearn for times whence Euclidian Becomes not rare but yeah, quotidian.

Mr Boyce

In fact, in the ten minutes I have spent googling this issue through my extensive research, I have uncovered a range of links between Mathematics and Literature which I shall now adumbrate.

Poems About MathematicsThroughout the centuries, there have been numerous poems written about Mathematics or using ideas from Mathematics. Geometry by Rita Dove, a former Ameri-can poet laureate, and Figures of Thought by Howard Nemerov, also an American poet laureate are just two instances. However, the poem Pi, written by the winner of the 1996 Nobel Prize in Literature, Polish poet Wi-slawa Szymborska, is perhaps the best example of the synthesis of Mathematics and poetry.

Pi

The admirable number pi: three point one four one. All the following digits are also just a start, fi ve nine two because it never ends. It can’t be grasped, six fi ve three fi ve , at a glance, eight nine, by calculation, seven nine, through imagination, or even three two three eight in jest, or by comparison four six to anything two six four three in the world. The longest snake on earth ends at thirty-odd feet.Same goes for fairy tale snakes, though they make it a little longer.The caravan of digits that is pidoes not stop at the edge of the page,but runs off the table and into the air,over the wall, a leaf, a bird’s nest, the clouds, straight into the sky,through all the bloatedness and bottomlessness.Oh how short, all but mouse-like is the comet’s tail!How frail is a ray of starlight, bending in any old space!Meanwhile two three fi fteen three hundred nineteenmy phone number your shirt sizethe year nineteen hundred and seventy-three sixth fl oornumber of inhabitants sixty-fi ve centship measurement two fi ngers a charade and a code,in which we fi nd how blithe the throstle sings!and please remain calm,and heaven and earth shall pass away,but not pi, that won’t happen,it still has an okay fi ve,and quite a fi ne eight,and all but fi nal seven,prodding and prodding a plodding eternityto last.

Surely a poem to delight both Miss Cox and Miss New-ton, with its numerical expertise and striking imagery.

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Poems That Use Mathematical Structures The systems that have been used in history to structure poetic metres are: the number of syllables (syllabic); the duration of syllables (quantitative); the number of stressed syllables, or accents (accentual); and combinations of the above.

To describe the pattern, the stressed and unstressed syllables are gathered into groups known as feet, and the number of feet to a line gives it a name:

3 feet: trimeter

4 feet: tetrameter

5 feet: pentameter

6 feet: hexameter

7 feet: heptameter

8 feet: octameter

We all know this, and probably highlight the suffi xes, pent, hex and oct. However, for something even more exciting, look at the syllables per line in this poem:

HE is famous but SHE is not. (8)Yet we once judged her (5)potential (3)greater (2)than (1)his. (1)

JoAnne Growney

1, 1, 2, 3, 5, 8

Can it be? A poem that uses the Fibonacci Sequence for a structure? What will they think of next?

Poems That Use a Mathematical(ish) Formula

The Oulipo, or Ouvroir de littérature potentielle (you can probably imagine how I pronounce this) was set up in France in 1960 by Raymond Queneau. One of the principle ideas of this group was the develop-ment of ‘constrained writing’ techniques. Perhaps their most outlandish project was the production of lipo-grammatic novels. The word lipogram is derived from Greek and literally means the omission of a particu-lar letter from a piece of work. Georges Perec wrote La Disparition (literally, “The Disappearance”) without using a single e in the entire novel. He did, however, retain the e’s in his own name, otherwise it would have been written by Gorgs Prc. Queneau summed up his theory in the 1963 essay “Potential Litera-ture,” stating that his objective was “To propose new ‘structures’ to writers, mathematical in nature, or to invent new artifi cial or mechanical procedures that will contribute to literary activity: props for inspiration as it were, or rather, in a way, aids for creativity.”

Anyway, getting back to the point, one of the most popular OULIPO formulas is “N+7,” in which the writer takes a poem already in existence and substi-

tutes each of the poem’s substantive nouns with the noun appearing seven nouns away in the dictionary.

Care is taken to ensure that the substitution is not just a compound derivative of the original, or shares a similar root, but a wholly diff erent word.

For example, Wordsworth’s Daff odils changes from:

I wandered lonely as a cloudThat fl oats on high o’er vales and hills,

To:

I wandered lonely as a clue That fl oats on high o’er vales and hindrance

The intention is that through experimentation students will ‘invent’ new poems and learn to experiment with language whilst at the same time practising numeracy skills.

In addition to re-writing poetry, another Oulipo technique is the prose snowball. Starting with a one word sentence, the story builds up sequentially with each sentence con-taining one word more than the last. Here is an example:

Cold.Numb fi ngers.My breath freezes.Can’t feel my toes.I have sent for help.Please God, when will it come?I have done nothing to deserve this.Stuck out here in the wind and snow. Alan Gillespie

Not only does this technique require some basic numer-acy skills but it encourages students to use a variety of sentences in their writing and helps them to build sus-pense.

Hopefully, this article has helped to dispel the idea that Mathematics and Literature do not mix and I look for-ward to seeing Mrs. Troughton teaching integral calculus through Shakespeare’s tragedies while Miss Levet explores feminist critiques of patriarchy in trigonometry.

Sources:

• http://mathdl.maa.org/images/upload_library/4/vol6/

• Growney/MathPoetry.html#OULIPO

• http://theamericanscholar.org/a-mindful-beauty/

• http://www.katherinestange.com/mathweb/index.html

• http://www.spoonbill.org/n+7/

• http://www.poets.org/viewmedia.php/prmMID/5916

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In PE By Ben Robinson

With PE being based on practical activity, it gives us the scope to transfer our knowledge and un-derstanding in a cross curricular way through a

kinaesthetic approach. This has allowed PE to deliver the whole school numeracy policy in variety of ways: score keeping, event/match timing or estimating distances for throws and jumps in athletics events.

The use of shapes and space plays a core role in our teaching methods and is an eff ective way for pupils to develop skills or tactics. Often pupils communicate through shapes when describing movements on a pitch. For example, students use a triangle when creating a 2 v 1 advantage in football or a straight back line when defending in rugby. This development allows pupils to physically establish shapes and visualise the movements that they will make. This visualisation technique cou-pled with memorising shapes or rhythms is transferable across diff erent subjects; through applying the process of visualisation and movement around a shape, it could perhaps be used to remember a timeline, or dates and events.

Numeracy can also be used as a basis for spe-cifi c units of work; one such unit is fi tness tests. This is taught in both Key Stage 3 and 4 and allows for pupil diff erentiation via the activity itself whilst enabling pupils to monitor their own individual progress.

The activity involves pupils performing and counting the number of repetitions performed during a variety of activities such as timed shuttle runs, press-ups or sit-ups. Extension tasks such as pupils working out averages, mean, median, mode and improvement tar-gets (if going over a series of lessons) can be conducted to introduce the concept of per-centages and ratios. The process can be taken further during Key Stage 4 and the information can be used as a means of data handling. Students can produce bar charts, line graphs, pie charts from their own results as well as a means of comparing others who have taken part in the tests.

The same strategy can be applied across a variety of subjects that use data or numbers as a comparison. Similarly, it can be used in a cross curricular way for pupils to establish their own AFL data across the year or Key Stage, this again not only links well with nu-meracy but also provides a good way of moni-toring progression and a visual aid to show the progress of each individual. Through embedding numeracy into our PE les-sons, we fi nd it has become a natural process and as a department we are comfortable in the delivery. Ultimately, students expect ele-ments of numeracy to be taught without there being an emphasis on the delivery but a natu-ral inclusion throughout the work.

Numeracy in the Classroom

6

Numeracy is incorporated through scale, use of coordinates, drawing and interpreting graphs, and the calculation and use of sim-

ple statistics (mean, medium, mode, etc).

Scale: a simple but popular exercise we do is for the pupils to map their desk surface – drawing to scale the desktop, exercise book, pencil case etc.

Co-ordinates: we use a number of Ord-nance Survey games including a robot game.

Graphs: usually a simple step by step ap-proach.

OS maps have blue lines called grid lines. These lines form grid squares. The num-bers given to each square are called Grid references.

So, what do gridlines mean?(Below explains how to read gridlines)

In order to remember, it along the corridor (East-ings) and up the stairs (Northings).

Lots of maps are divided up into equal sized squares. To help fi nd places on a map each square has a number that can be used to identify an exact point.

In GeographyBy Martin Squires

What direction do these lines go in? East

These lines are called Eastings

What direction do these lines

go in?

North

These lines are called Northings

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8

Using numeracy skills in History... here is a game designed for students to use numeracy skills, while we learn about trade in the Roman Empire.

Could you be a Roman Trader?

In History...

9

1) Understanding: what is trade? Import and export?

IMPORTSGood brought into a

country.e.g. Wine brought into

Britain from France.

EXPORTSGood sold out of a

country.e.g. Cars made in

Britain and sold to Spain.

2) Roman Trade game?Rome was the centre of the Empire’s trade. As the map shows, loads of diff erent materials, products and people were traded from diff erent areas of the empire. Traders would travel to far fl ung reaches of the Empire and buy things which they would sell on in Rome for a profi t.

How well do you think you would succeed as a Roman trader? Would you make a huge profi ts? Or would you lose all you money?

1. You have 40 denarius to INVEST im-ports from the Empire.

2. You can spend the money on up to 3 diff erent products.

3. Over the course of the year each product will either stay at the same price (you make no profi t), go up in price (you gain a profi t) or go down in price (you will lose money).

4. Whatever money you have (either gained/left over) you can re-invest the next year.

5. Use the INVESTMENT SHEET to plan your trad-ing.

6. Whoever has the most money left at the end is the RICHEST ROMAN

TRADER!!!

40 d +15 d

Horses Greece 15 d 25 d

Slaves Germany 15 d 25 d

Dyes Africa 5 d 5 d

Tin Britain 5 d 0 d

INVESTMENT SHEET

99

40 d +15 d

Whilst there are many traditional ways of incorporating numeracy into Modern For-eign Language lessons, such as completing

simple sums, writing about birthdays and working out change from shopping transactions, there are also other, less conventional ways to make nu-meracy altogether more active. A personal favour-ite is ‘Time Ballet’, which is popular with Year 7 and Year 11 students alike and helps learners to consolidate their understanding of the time in the target language.

Forget images of a pirouetting Darcey Bussell wearing a vintage Rolex, this activity simply re-quires students to use their arms as the hands of a clock, and display the time they hear called out in the target language. I prefer to play music whilst completing the activity, but that’s entirely optional. Not only does this activity give learners the chance to practise their listening comprehen-sion skills, but it also enables the teacher to as-sess understanding instantly.

Clearly Time Ballet itself seems largely irrelevant to subjects beyond MFL, but there could well be some scope for acting out various mathematical processes or symbols to help consolidate stu-dents’ understanding in other lessons. I’ll leave you to refl ect on that in your own time…

By Niamh Bland

Quelle heure il est?Telling the time in French...

Quelle heure il est?

What time is it?

Il est...It is...

une heure et quart

1 o’clock and a quarter

for us this is quarter past one

une heure-et-demie

1 o’clock and a half

for this this is half past one

un heure moins le quart

1 o’clock less a quarter

for us this is quarter to one10

We teach numeracy

using a variety of

activites - bingo, mini

whiteboards, fl ashcards etc. We

also use sites like www.linguascope.

com whee students can watch a

‘presentation that introduces the num-

bers in the foreign languages and

the provides various

activites to practice.

By Jo Johnston

Year 7learning numbers in a foreign

language, (and doing simple sums in then target language) date and times

and the 12 hour clock.

Year 8Shopping, working out euros and changes, the 24 hour clock, pocket monet, saying how tall you

are, and quantities.

Year 9More about the time (e.g, arranging

to meet) and longer numbers.

When numbers are a little diff erent

Most mainland European countries use the 24hour clock so sometimes we need to ‘teach’ that as a concept before we can use it in the Target Language readily.

We also use it In dates/birthdays etc in English (and German), we use ordinal numbers (e.g. 3rd May) whereas in French, Spanish and Italian we use cardinal numbers (3 mai/mayo/maggio) with the exception of the month (le premier/ el prim-ero/ il primo).

When we teach time in French, Spanish and Italian for ‘10 to [the hour]’ in English is ‘half to’ in German. So 10.30 in German is half to eleven.

Literacy point here... in French, Spanish and Italian there are NO capitals for the days or months. In German every noun has a ca[ital letter!

By Jo Green

11

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We found that students did not see the relevance of a numeracy objective and would rather have the skill pointed out while they were undertaking a particular activity.

Students also suggested a tick sheet with numeracy skills identifi ed which could be stuck into their subject books and used as a part of a peer/self assess-ment activity.

Following this study we have created a student friendly mind map using the student perceptions of numeracy. We hope you fi nd it useful.

I only really recognised it as numeracy look-ing back on it

Reading graphs and charts

Prioritising information

Trial and error

how students see numeracy...

Gathering information

We held an initial focus group where we asked students what numeracy was and in which subjects they

thought they used numeracy skills.

By working in a group, students were able to identify a variety of skills associated with numeracy. They did struggle initially with seeing how numeracy was embedded across their curriculum.

One student commented: “you don’t think about it. It’s a common thing. It’s only in Maths you think about it”. Due to these re-sponses we asked students to spend a week identifying all of the numeracy skills they have discussed in the focus group.

Following the week of information gather-ing, we held another focus group where students mind mapped their fi ndings.

These fi ndngs have been summarised on the opposite page. We asked students if this study had made a diff erence to their understanding of numeracy, and if they had any suggestions for making numeracy more explicit .

Sequencing data

Problem solving

Applying method

Filtering data

Estimation

A s part of TELL’s numeracy focus we decided to carry out a study with six Year 10 students. Students were allowed to keep a numeracy diary throughout the week, identifying any numeracy skills they were asked to

use. However, most importantly, through our study we were able to help students to be aware of numeracy skills across the curriculum.

Numeracy By Sally Newton and Meera Chudasama

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Comparing data collected by

other peoples.

e.g. PEE paragraph structure is

an acronym for Point, Evi-dence and Explain. A method that students apply towards

writing essays.

applying uses and gratifi ca-tion’s theory to own

work

e.g. calculating the

heart rate per minute

MFLSentence structure, e.g, in German, the verb always at the

end of the sentence.

ICTCollecting data,

using formulas and codes to generate

data and break-down data.

Interpreting data,

e.g. Sources in History

V&EIdentifying prob-lems and solving

problems that apply to real life situa-

tions.

e.g. identifying dangers in the work-

placeand how to avoid/fi x them. Being responsible in

the workplace.

GEOGRAPHYFiltering information, reading graphs and charts, and under-

standing strategies.

BUSINESSSTUDIES

Requires calculating profi t, loss, break-

even, as well as

estimation.

e.g. out of the data in source 1,

identify what are human & environmental factors

that affect fl ooding

MEDIAInterpreting infor-

mation from media products, applying method in creating

media products.

ARTDrawing to scale,

using ration, under-standing proportion, and applying artist

technique.

SOCIOLOGYReading and inter-preting graphs, as well as collecting

data.

PECalculation,

prediction, and trial and error ENGLISH

Applying method onto answer (e.g PEE paragraph structure), interpeting informa-tion, and predicting

narrative

SCIENCEConducting

investigations, predicting results, trail and error, and

anaysing data collected

HISTORYInterpreting

information, and sorting information in

chronological order.

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E.g. Watching fi lms

or reading articles to gather information, and create your own

work in a similar style.

E.g. Predicting the results of an experiment

E.g. Making an image twice the size using

perspective and ratio methods.

Using an artist’s technique in your own work

allows you to understand a method

of applying a medium.

E.g. Creating

timelines helps you puts historical

events in chronological

order.

MFLSentence structure, e.g, in German, the verb always at the

end of the sentence.

MEDIAInterpreting infor-

mation from media products, applying method in creating

media products.

ARTDrawing to scale,

using ratio, under-standing proportion, and applying artist

technique.

SOCIOLOGYReading and

interpreting graphs, as well as collecting

data.

SCIENCEConducting

investigations, predicting results, trial and error, and

analysing data collected

HISTORYInterpreting

information, and sorting information in

chronological order.

Numerthe student persepctive

DRAMAInquiry based learn-ing. Problem solving

when scene do not go to plan.

14

racy

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total expenditure, fi nding out if you have made a profi t, loss or

if your company is breaking even.

E.g. Identifying

problems in the work place, and resolving them through prob-

lem solving tech-niques.

Read-ing population

charts, and being able to interpret information from

the chart

Using diff erent writing

techniques for for diff erent purposes,

e.g. to describe.

Apply-ing your own

knowledge and understanding to

written texts.

E.g Calculating in-crease and de-

crease of heart rate before and after

excerise.

ICTCollecting data,

using formulas to generate data and

breakdown data.

V&EIdentifying prob-lems and solving

problems that apply to real life situa-

tions.

GEOGRAPHYFiltering information, reading graphs and charts, and under-

standing strategies.BUSINESSSTUDIES

Requires calculating profi t, loss, total ex-penditure, as well as

estimation.

PECalculation,

prediction, keeping score, and trial

and error

ENGLISHApplying method

onto answer (e.g PEE paragraph structure),

interpeting information, and predicting

narrative

DTUsing perspective, measurments, and

angles when creating and

designing.

MUSICCounting in

beats. Breaking music in to

sections.

15

Inquiry

Whilst acting in role, students use their inquiry based learning skills to solve the problems in our Yr 9 unit: ‘Lost ’...

Are you really alone on this

seemingly deserted island?

What type of island is this?

What is your fear?

What is this hatch?Who, or what, are the ‘others?

16

based learning

The concept of a silent debate sounds like a con-tradiction of terms – how can you debate silently? Nonetheless it is a teaching tool that I fi nd works

in any concept, with any class and any year group. The principle of the activity is that students are given an inquiry question at the start of the lesson, which they investigate by looking at smaller questions. They then build on this through the silent debate, which allows them to see the wider issue, and gain a broader under-standing of the question.

I tend to use it part way through a lesson so that students can use the skills and knowledge they have acquired at the start of the lesson and then they can use the silent debate to link back to the question at the end. The silent debate works by having questions that stimu-late a discussion between the students. I use Bloom’s taxonomy to diff erentiate the questions, so all students can access the task. This means they don’t have to an-swer all the questions but can pick and choose the ones they feel most able to debate. I tend to put the ques-tions at the top of big pieces of sugar paper so there is plenty of room for information to be recorded and aim to have no more than 4 people trying to write at the same time, so for a group of 30 I would have approxi-mately 8 questions.

Once you have explained the principle of the task – that students need to record their opin-ions in silence and then move onto another question – you can also get involved. This is a perfect way to check understanding and correct incorrect information swiftly. You can also push students on in their learning by adding further questions to their responses.

So in one fell swoop you are diff erentiating, giving immediate feedback and achieving eff ec-tive progress of all students. In order to see the context of how I would use a silent debate I have included a lesson over-view that I have used with a year 13 psychol-ogy group:

1. Starter – inquiry question with a hypothesis (To what extent is the media responsible for addiction?)2. Card sort on diff erent factors using a venn diagram.3. Refl ection on hypothesis.4. Silent debate.5. Refl ection on hypothesis.6. Class discussion (I get the students to take down one of the sheets of paper in pairs and pick out the points they most and least agree with to help stimu-late discussion). 7. Final refl ection on hypothesis.

As stated earlier, I have used this technique with numer-ous classes, ranging from a set 4 year 9 history group (of just 13 boys), to a top set year 7 group; KS3 to KS5 history and psychology – it has consistently worked for me and my students have really enjoyed the concept of debating silently.

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